Sepp Blatter's decision to resign as president of Fifa is "brilliant for world football", says Football Association chairman Greg Dyke.
The FA had opposed the re-election of Blatter, who last week won a fifth term in office before his sudden U-turn.
Dyke told the BBC: "This is great news for football. It should have happened years ago.
"There has to be a root-and-branch investigation of Fifa. It has all got to be transparent in the future."
Dyke added: "It now means that we can get someone in to run Fifa. We can get in there and find out where all the money has gone over all these years and sort it out for the future."
Blatter was re-elected despite seven top Fifa officials being arrested two days before the vote as part of a US investigation.
But after admitting his mandate "does not appear to be supported by everybody" he called for an extraordinary Fifa congress "as soon as possible" to elect a new president.
The view from around the UK and Ireland
Football Association of Wales chief executive Jonathan Ford said he was "amazed" by Blatter's announcement that he is to resign.
Ford told BBC Radio Wales: "He's been a fantastic leader, but arguably one that probably stayed on a little too long.
"Let's place credit where credit is due. He's been at the helm and taken world football to be what it is today."
Football Association of Ireland chief executive John Delaney said: "These are changes that we had called for and had hoped would come. We believe there is now an opportunity for real change and reform at Fifa.
"It is important that this opportunity to change the culture within Fifa at the highest levels is not passed up."
|Fifa corruption claims - key questions answered|
|Who does Sepp Blatter think he is?|
|Blatter in quotes|
Scottish FA chief executive Stewart Regan said he was keen to discuss what should happen next with other Uefa associations.
Regan added: "We, like many other national associations, have maintained that the governance of world football's governing body requires to be reformed - especially in light of recent allegations - and we are glad Mr Blatter now shares this view.
"We will discuss today's developments and any collective next steps with all other Uefa associations at next weekend's Champions League final in Berlin."
'Change is finally coming'
Uefa president Michel Platini, who had urged Blatter not to stand for re-election and to quit following the arrests in Switzerland, said: "It was a difficult decision, a brave decision, and the right decision."
Former Portugal international and former world player of the year Luis Figo, who withdrew his candidacy for Fifa president a week before the election, said via Facebook: "A good day for Fifa and for football. Change is finally coming.
"Now we should, responsibly and calmly, find a consensual solution worldwide in order to start new era of dynamism, transparency and democracy in Fifa."
Blatter move prompts Gill rethink
Football Association vice-chairman David Gill intends to reconsider his decision not to sit on Fifa's executive committee following Blatter's move to stand down.
Gill, the former chief executive of Manchester United, said: "Naturally, I fully welcome today's news as a major step forward for Fifa on the road to proper reform.
"I simply could not countenance serving on the Fifa Executive Committee alongside Mr Blatter.
"I respect his decision but am pleased he is standing aside and by the clear determination for real change within Fifa. This in turn allows me to reconsider my position."