Liberal Democrat David Laws has resigned as Chief Secretary to the Treasury after admitting he claimed expenses to pay rent to his partner.
He said he could not carry on with the "crucial work" on the Budget while dealing with the implications of the revelations in the Daily Telegraph.
He had earlier apologised and said he would pay back the £40,000 he claimed.
Prime Minister David Cameron and his deputy Nick Clegg paid tribute to Mr Laws saying they hoped he would return.
The Yeovil MP said he wanted to keep his relationship with James Lundie private.
Mr Laws is the first resignation to hit the coalition government, just three weeks after it was formed.
He was one of the Liberal Democrat negotiators who hammered out the deal before joining the cabinet as a key member of Chancellor George Osborne's team.
Mr Laws said he had informed both David Cameron and Nick Clegg, but it had been "his decision alone".
In his resignation letter to Mr Cameron, he wrote: "The last 24 hours have been very difficult and distressing for me, and I have been thinking carefully about what action I should take in the interests of the government, my constituents and - most important of all - those whom I love.
"I am grateful for the strong support which I have received from my friends, family, and from you, the deputy prime minister and the chancellor. This support has been incredibly important, but nonetheless, I have decided that it is right to tender my resignation as chief secretary to the Treasury."
Explaining his decision, he said: "I do not see how I can carry out my crucial work on the Budget and spending review while I have to deal with the private and public implications of recent revelations.
"I cannot now escape the conclusion that what I have done was in some way wrong, even though I did not gain any financial benefit from keeping my relationship secret in this way."
He added: "Most importantly, I have an overriding responsibility to those I love most, and who I feel I have exposed to scrutiny in this way.
"I have pursued a political career because of my sense of public duty, but I have too often put this before the interests of those I love most. It is time to redress the balance."
Lib Dem Scottish Secretary Danny Alexander will take over the post, Downing Street has announced.
Responding to Mr Laws' resignation letter, Mr Cameron said he was an "honourable man", adding: "I hope that, in time, you will be able to serve again."
Lib Dem Deputy Prime Minister Nick Clegg said he had always admired Mr Laws' integrity and he hoped he would one day be able to return to government.
He said Mr Laws' privacy had now been "cruelly shattered".
Mr Cameron wrote: "The last 24 hours must have been extraordinarily difficult and painful for you.
"You are a good and honourable man. I am sure that, throughout, you have been motivated by wanting to protect your privacy rather than anything else.
"Your decision to resign from the government demonstrates the importance you attach to your integrity.
"In your short time at the Treasury, you have made a real difference, setting the government on the right path to tackle the deficit which poses such a risk to our economy."
Mr Clegg said: "I very much hope that when those questions are answered there will be an opportunity for him to rejoin the government because, as everyone has seen in recent weeks, he has so much to contribute to national life.
"When all is said and done, this has come about because of David's intense desire to keep his own private life private. His privacy has now been cruelly shattered.
"I'm sure I speak on behalf of all fair-minded people when I say that I hope that David, and all those people close to him, will now be granted the privacy which he has always craved."
The chancellor said he was "very sorry" to lose Mr Laws from the Treasury.
Mr Osborne said: "It was as if he had been put on earth to do the job that was asked of him.
"I spoke to David several times over the last 24 hours and I have a huge admiration for the way he has conducted himself in the most difficult circumstances.
"I completely understand and respect his decision to step down. Public life should have a future place for such an honourable, talented person."
Former Liberal Democrat MP Lembit Opik who is a friend of David Laws, said he was the victim of a "witch hunt".
He said: "I think this is a national tragedy, not least because it suggests that - on matters which are nothing to do with a person's personal competence to do a job - they can still be pushed out of Parliament."