In a letter to the U.K. prime minister David Cameron, she said the controversy "has become a distraction from the vital work this government is doing."
Cameron told the British media he was sorry to get the letter, but accepted her decision.
Miller was cleared last week by the House of Commons committee on standards of deliberately submitting expenses claims to which she was not entitled, but she was ordered to say sorry over her attitude to the inquiry which had breached the ministers' code of conduct.
Miller was also ordered to repay $9,600 (£5,800) to cover over-claiming of house loan mortgage expenses after she failed to cut her claims as interest rates fell.
In a short statement, Miller told MPs she apologized "unreservedly."
Calls for her resignation then gathered pace with senior politicians from across the parties and the press voicing the opinion she should go.
Miller's duties included formulating the government's policies on press regulation following the Leveson inquiry into press standards after the phone-hacking scandal that engulfed Rupert Murdoch's News International.
Cameron's official spokesman said the prime minister and Miller discussed her future on Tuesday night and her resignation was confirmed on Wednesday morning.
The decision comes a day before Parliament breaks for its Easter recess and ahead of a session of Prime Minister's Questions, at which Cameron is expected to come under pressure over the row.
In the immediate aftermath of the apology less than a week ago Cameron said Miller was doing an "excellent job as culture secretary and will continue to do that" and with her apology, "people should leave it at that."
The investigation into Miller's expenses' claim was prompted by a formal complaint in December 2012 from Labour party parliament member, John Mann.
This followed reports she had allowed her parents to live in a property on which she claimed second home allowances between 2005 and 2009.
The committee rejected the charge that she or her parents had benefited financially from the arrangements.
Miller speaking in Parliament April 3 said: "The report resulted from an allegation made by the member for Bassetlaw [Mr Mann]. The committee has dismissed his allegation. The committee has recommended that I apologize to the House for my attitude to the commissioner's inquiries, and I of course unreservedly apologize. I fully accept the recommendations of the committee and thank them for bringing this matter to an end."
It ended, instead, in her resignation.