Prime Minister David Cameron and the Queen were among those to pay tribute to Andy Murray's Wimbledon victory.
Sport stars and celebrities have also praised the 26-year-old Scot after he became the first British men's winner since Fred Perry in 1936, beating Novak Djokovic in straight sets.
The prime minister told the BBC: "It was an amazing performance from Andy Murray, but also an amazing day for British tennis and for Britain. He never gave up and it was magnificent.
"It was a privilege to watch Andy Murray making history."
BBC Royal correspondent Peter Hunt revealed: "The Queen has sent a private message to Andy Murray."
Cyclist Sir Chris Hoy, an Olympic champion like Murray, was on Centre Court to witness his compatriot's moment of triumph.
"It has been a privilege to witness it and be in the box with family and friends, to share that very special moment," he told BBC Radio 5 live.
"I know how much it means to him, his mum and everyone. I suppose there are times when they wonder if it is ever going to happen. They kept the faith and he was just supreme out there. It wasn't a walk in the park. It was a real battle.
"Andy is tennis, Andy is Wimbledon for the UK. There is only one person really that expectation lies on. I was a member of a team so if I didn't succeed it wouldn't be the end of the world for the whole nation.
"I have no idea how he deals with that expectation. Now after 77 years we can celebrate a British winner of Wimbledon, fantastic."
Murray converted his fourth championship point in a dramatic final game to win 6-4 7-5 6-4 and claim his second major title.
He is Scotland's first Wimbledon singles champion since Harold Mahony in 1896 and the first Briton to win since Perry captured his third title there in 1936.
Perry's daughter, Penny Perry, told the BBC she found the experience of watching Murray's triumph "surreal".
She said: "I'm not sure what I was thinking. I was watching in a bit of a daze, expecting the inevitable. I am stunned.
"Dad would have been stunned. We, as a family and the nation, have spent so long waiting, it is almost wow, now it has happened we are not too sure how to react.
"Fred was fiercely patriotic and this is fabulous for Britain. It is fantastic for British tennis. He spent 40, 50, 60 years being asked every year 'where is the next Brit coming from?'. He couldn't answer then and today we have found it.
"I think it is amazing, it is fabulous, congratulations to him."
Former England striker Gary Lineker and ex-Liverpool boss Kenny Dalglish were among those from the world of football to praise Murray's triumph.
Gary Lineker said on Twitter: "What a fighter! What a talent. What a man. What a winner! Wimbledon champion! Congratulations!"
Dalglish added: "Unbelievable. What a fantastic story. Magnificent. What fantastic dignity from the loser. Off to celebrate. Ya beauty."
Manchester United defender Rio Ferdinand said: "Hard work pays off. Andy_murray congrats and well deserved fella."
Britain's number one women's tennis player Laura Robson, who herself reached the second week of Wimbledon, simply tweeted: "So good!!!!!!!!!!!!!! #andymurray #proud."
Robson won Olympic silver with Murray in the mixed doubles at London 2012 just hours after he took the singles title with a straight-sets victory over Roger Federer.
His fellow Olympic champion Greg Rutherford, who won long jump gold, said: "Unbelievable amazing awesome and all the great descriptive words!! Andy Murray has done it!!"
Murray's victory also drew tributes from celebrities away from the world of sport.
Television presenters Ant and Dec said: "Get in Andy Murray!! What a champion's performance. And what a gent Novak Djokovic is. Great match. Great winner."
Scotland's First Minister Alex Salmond told the BBC News Channel: "This young man deserves every bit of his success, he's not just overcome adversity it is all about constant improvement.
"He does everything to continue his game, if he has to build himself up, he builds himself up, if he has to train himself to do things he didn't like doing, he does that.
"Everything about him is about self-improvement, and he deserves every bit of his success. I've been watching him for 10 years, he is a different man out there and he's different to last year, he's getting better all the time."