Brazil forward Neymar said he needed a new challenge, as he joined Paris St-Germain from Barcelona for a world record fee of 222m euros (£200m).
The 25-year-old won seven major trophies in his four seasons at the Nou Camp, including the Champions League once and La Liga twice.
He said his father, Neymar Sr, wanted him to stay at Barcelona.
"I have won all that a player can win," said Neymar, who will earn 45m euros (£40.7m) a year on a five-year deal.
Writing on Instagram, he added: "I have conquered everything an athlete can conquer. I have lived unforgettable moments. But a player [me] needs challenges.
"And for the second time in my life, I'll contradict my father."
Neymar's transfer smashes the previous record set when Paul Pogba returned to Manchester United from Juventus for £89m in August 2016.
His £782,000-a-week wages mean PSG's total outlay is £400m.
The French side have called a news conference for 12:30 BST on Friday, and Neymar will be introduced to fans at PSG's first game of the season against Amiens at Parc des Princes on Saturday.
PSG reached the last eight of the Champions League last season - knocked out by a Neymar-inspired Barcelona - and were beaten to the French title by Monaco.
Neymar said he has joined "one of the most ambitious clubs in Europe".
"Paris St-Germain's ambition attracted me to the club, along with the passion and the energy this brings," he added.
"I feel ready to take the challenge. I will do everything I can to help my new team-mates."
- Analysis: What now for Barcelona? What was the moment Neymar decided to leave?
- 222m euros for a footballer - how do you feel?
- Brazil forward to earn 45m euros a year at PSG
A late snag?
After weeks of speculation, Neymar arrived at Barcelona's training ground on Wednesday with his father and representative, and told the Spanish club he wanted to leave.
He was then given permission by Barca manager Ernesto Valverde to leave to "sort out his future".
In Spain, a release clause can only be activated by a player buying himself out of his contract.
But when Neymar's lawyers attempted to make the deposit on Thursday, La Liga officials rejected the payment. Further statements followed from all sides as the negotiations continued.
La Liga believes PSG are violating Uefa's Financial Fair Play (FFP) rules and Barcelona previously said they would report PSG to European football's governing body Uefa for an FFP breach.
PSG believes La Liga was acting unlawfully, while the French league (LFP) said it was "surprised" and urged its Spanish counterpart to "abide by the Fifa rules".
Unable to get La Liga to take the payment, Neymar's representatives paid the 222m euros (£200m) at Barca's offices instead.
So FFP... who is right?
FFP rules, first implemented during the 2011-12 season, stipulate European clubs cannot outspend what they earn by more than 30m euros.
PSG are backed by money from Gulf state Qatar, and La Liga president Javier Tebas has accused the French club of "financial doping".
It is the first time PSG - ranked the 11th most valuable club in the world by Forbes - have broken the global transfer record, with Real Madrid paying five of the past six highest fees.
- Reality Check: Can PSG get away with 222m euros fee?
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Stepping out of Messi's shadow?
Neymar's departure from Barcelona breaks up the feted attacking trident he formed with Argentina captain Lionel Messi and Uruguay forward Luis Suarez.
On Wednesday, Messi posted on Instagram: "It was a great pleasure to have shared all these years with you my friend Neymar. I wish you good luck in this new stage of your life." Neymar replied: "Thank you brother. I will miss you."
Then, after completing the move, the Brazilian posted his own message, calling the Argentine "the best athlete I've ever seen in my life".
"Lionel Messi became my team-mate, and my friend on and off the pitch," he wrote. "I am proud to have played with you. We formed an attack with Luis Suarez that will endure forever.
"I achieved everything a sportsperson can achieve. I played with these guys in video games. I lived unforgettable moments in a city that is more than a city - it's a homeland.
"Barcelona and Catalonia will always be in my heart but I need a new challenge. PSG offered a bold new way forward and I'm ready. Right now I feel in my heart that it's time to go."
- Since joining Barca in 2013, Neymar scored 68 goals in four full seasons - behind Cristiano Ronaldo (139), Messi (134), Luis Suarez (85), Antoine Griezmann (76) and Athletic Bilbao's Aritz Aduriz (70)
- In that same period, he had the fifth most direct assists with 38 - again behind Messi (54), Atletico Madrid's Koke (45), Suarez (43) and Ronaldo (42)
- In chances created in that time (287), he was second only to team-mate Messi (326)
- He had the highest number of chances created last season (91) - more than any other PSG player (Angel di Maria had 78)
- Edinson Cavani scored almost three times as many league goals (35) than Neymar (13) last season
Neymar in profile
- Born in Mogi das Cruzes, a suburb of Sao Paulo, on 5 February 1992
- Started his career at Santos after signing a professional contract in January 2009
- Remains Santos' leading goalscorer in the post-Pele era with 138 goals in 229 matches
- Real Madrid, Chelsea and Manchester United were all linked before he eventually signed for Barcelona in June 2013 at the age of 21
- He made his Barca debut against Levante in August 2013 and went on to score 105 goals and provide 80 assists in 186 games for the Catalan club
- He won two La Liga titles and one Champions League
- Made his international debut aged 18 and he has scored 52 goals in 77 games for Brazil
|Neymar at Barcelona last season|
|Games||Minutes played||Goals||Minutes per goal||Assists|
What happened the last time Neymar was signed
When Neymar joined Barcelona in June 2013, the club said they paid a total of £48.6m.
But after Barca refused to offer more details, an investigation was started by the Spanish prosecutor into whether the club had defrauded the treasury of unpaid tax.
The president Sandro Rosell, who personally oversaw the pursuit of Neymar, eventually resigned - though he said it was for personal reasons - and his successor, Josep Maria Bartomeu, revealed the true cost of the deal was actually £71.5m.
- Neymar's father got £33m fee, plus £2m in "agent fees"
- Santos got £14m, plus £6m by giving Barca an option on future Santos players
- The player got an £8m signing-on fee, plus £9m a year in wages over five years
- Neymar's charitable foundation in Brazil also received £2m
History of the world transfer record
In 1975, Italian Giuseppe Savoldi became football's first £1m player with his move from Bologna to Napoli. And Britain followed suit four years later, when Nottingham Forest paid Birmingham City £1.2m for England forward Trevor Francis.
Only two players have broken the transfer record twice: Argentina legend Diego Maradona and Brazil great Ronaldo.
Maradona moved from Boca Juniors to Barcelona for £3m in 1982, before joining Napoli two years later for £5m. Ronaldo joined Barcelona for £13.2m in 1996, but left after just one season to join Inter for £19.5m.
Brazil winger Denilson (£21.5m), Italy striker Christian Vieri (£32m), Argentina forward Hernan Crespo (£35.5m), Portugal winger Luis Figo (£37m) and France playmaker Zinedine Zidane (£46m) all raised the bar over the next three years.
Brazil midfielder Kaka (£56m) breached the £50m barrier in 2009 before his new club Real Madrid broke the record again by signing Portugal forward Cristiano Ronaldo from Manchester United for £80m three weeks later.
The Bernabeu club beat their own record again with their £85m deal with Tottenham for Wales forward Gareth Bale in 2013 - before Manchester United paid £89m for France midfielder Pogba last summer.
Reaction & #NeymarMaths
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Manchester United manager Jose Mourinho: "Expensive are the ones who get into a certain level without a certain quality. For £200m, I don't think [Neymar] is expensive.
"I think he's expensive in the fact that now you are going to have more players at £100m, you are going have more players at £80m and more players at £60m. And I think that's the problem.
"So I think the problem is not Neymar, I think the problem is the consequences of Neymar."
Liverpool manager Jurgen Klopp: "I thought Fair Play was made so that situations like that can't happen. That's more of a suggestion than a real rule."
Lille director general Marc Ingla, a former Barcelona vice president: "It's a blow for Barcelona. Neymar is an accelerator to this bright future of Ligue 1. The young talent pool we have here is the best in Europe. For sure we can still compete with PSG. Once you get on the pitch it's 11 v 11 and all the transfer fees and salaries narrow a bit."
Barcelona's Arda Turan: "It was a great pleasure to have lived all those unforgettable moments with you my brother. Wish you the best. Always..."
What would 222m euros buy you?
- Five Huddersfield Towns - the Premier League new boys are valued at £44m
- Effectively, it would buy you Monaco, the 19th most valuable club in the world based on figures from Transfermarkt
- You could pay Premier League champions Chelsea's prize money and broadcast fees for last season and still have change
- Or how about buying 1.5 million men's PSG shirts - the club's official store are selling the 2017-18 home jersey for 140 euros
- In fact, why not splash out on 2 Kensington Palace Gardens. Steel magnate Lakshmi Mittal bought the London property in 2004 for £57m (76m euros in today's market)
- Or invest in 1,032 trips to space with Virgin Galactic. A ticket for Sir Richard Branson's commercial space-line currently costs $250,000
BBC Radio 5 live sports news correspondent Richard Conway
Rêvons Plus Grand!", PSG's motto, is hard to avoid at their stadium, Parc de Princes.
Translated? "Dream Bigger!".
Signing Neymar, and obliterating the transfer world record, is certainly living up to that self-imposed ideal.
The club's owners, Qatari Sports Investment (QSI), are the upstarts within the European game and are determined to disrupt the old order.
QSI is an arm of Qatar's sovereign wealth fund - so PSG's ambitions are backed by the enormous natural gas wealth of the Gulf state.
Qatar is locked in a bitter dispute with its Arab neighbours right now - so this transfer has a distinct political overtone as it seeks to show it will not be diminished or cowed by an on-going trade blockade and a diplomatic war of words.
Having secured the World Cup in 2022, PSG is seen in Doha as one of the ways through which the state can achieve its ambitions.
And in Neymar they now have a player it hopes can bridge the gap between Champions League wannabes and serial winners.
Progress towards that target has not been easy so far. Millions spent in transfer fees has delivered plenty of domestic silverware. It is not the success the club truly craves.
A spate of recent quarter-final defeats and last season's second-leg capitulation to Barcelona in the round of 16 does not reflect the high ambitions of those in charge.
The talk in Paris is of building a dynasty, not merely creating fleeting moments of hope and glory.
As for Uefa's financial fair play? The regulations have certainly tempered PSG's elaborate spending in recent seasons but Neymar's arrival represents a serious challenge to the club in this respect alongside Uefa's credibility.
The value of this deal - fee and wages - must pass the necessary tests. There's confidence within PSG's boardroom that it will not be a significant issue but their accountants will perhaps be as busy as the first team squad in coming months.
In the end, this is an era-defining transfer on a par - in terms of its significance - with Maradona to Napoli, Shearer to Newcastle, Zidane, Ronaldo and Bale to Real Madrid or Pogba to Manchester United.
Those moves all had sporting ambition at their heart. This transfer, for now, is perceived more as a triumph of political and financial considerations.
But this is football. And ultimately this deal will not be judged in the governmental salons of Doha nor on a spreadsheet. Instead, success must be delivered through PSG capturing the club game's greatest trophy.
Brazilian journalist Fernando Duarte: "This is simply the biggest ever deal in football history.
"We're talking about a player who has the potential to be one of the best in the world. He has the marketing potential, he's a natural, unlike Lionel Messi for example who always looks awkward on camera.
"Why should Brad Pitt get $20m for a movie and a football player, who is not going to be playing in his 40s like many sporting stars, shouldn't?
"One year before the World Cup, he's going to a club where everything will be resting on his shoulders. If PSG win the Champions League, it will be Neymar's plaudits. If PSG fail, it will be Neymar's fault."
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