The MP for Corby is moving to New York with her three children to be close to her husband Peter Mensch, the manager of rock bands Metallica and the Red Hot Chili Peppers.
This will trigger a by-election in her Northamptonshire constituency.
Before entering politics, Mensch found fame as an author of 'chick-lit' fiction, under her maiden name Bagshawe.
She was among the most high profile Tories to enter the Commons in 2010, but was even more in the spotlight last year during the investigation of the phone hacking scandal by the Commons culture committee, of which she is a member.
Mensch was also recently involved in the launch of 'Menshn.com', a new social network that aims to become a more debate-focused version of Twitter.
In a resignation letter sent to prime minister David Cameron, Mensch said that she was finding it difficult to juggle her family commitments with the demands of a political career.
She described the decision to quit the government as "devastating but necessary".
In his response, Cameron praised Mensch for her "truly inspiring" time as an MP.
"It is with enormous regret that I accept your resignation as the MP for Corby and East Northamptonshire, a seat that had been Labour for thirteen years before you," he said.
"I do so only because I wish to support you in acting in the best interests of your family, which must come first."
The by-election will be held on November 15.