In a letter to Prime Minister David Cameron, Mrs Miller said the controversy "has become a distraction from the vital work this government is doing".
In her resignation letter, the Basingstoke MP told Mr Cameron she was "very grateful" for his personal support.
"But it has become clear to me that the present situation has become a distraction from the vital work this Government is doing to turn our country around," she added.
She defended her work on press regulation - which allies have suggested has resulted in a media "witch hunt" against her.
"Of course, implementing the recommendations made by Lord Justice Leveson on the future of media regulation, following the phone hacking scandals, would always be controversial for the press," she wrote.
"Working together with you, I believe we struck the right balance between protecting the freedom of the press and ensuring fairness, particularly for victims of press intrusion, to have a clear right of redress."
Mr Cameron told her it was "important to be clear that the Committee on Standards cleared you of the unfounded allegations made against you, a point which has been lost in much of the comment in recent days".
The standards committee ordered her to repay £5,800 in overclaimed mortgage interest and say sorry on the floor of the House - an apology which has been widely criticised for its tone and brevity.
"As you leave the Government, you should be proud of your service on the Frontbench and in Opposition," Mr Cameron said - including steering through gay marriage and press regulation.
"I am personally very grateful for the support you have always given me, and which I am sure that you will continue to give.
"I hope that you will be able to return to serving the Government on the Frontbench in due course, and am only sad that you are leaving the Government in these circumstances."