However, if he did so, he would have to combine being an MP with continuing as Mayor of London until his term expires in May 2016.
If he returns to the Commons he will want to find a seat which is in easy rich of central London. The seat in Hertsmere would offer just that for Mr Johnson.
Mr Clappison, who has been an MP for 23 years, is a well-regarded member of the Home Affairs select committee and the European Scrutiny committee.
In a letter to Mr Cameron, Mr Clappison said: “It is difficult letting go but I do feel now is the time to move on. There is a world elsewhere.”
Separately, Mike Weatherley, MP for Hove and Portslade and one of the intake at the 2010 general election, also said he was quitting as an MP next year.
In his letter to the Prime Minister, Mr Weatherley said he was leaving for personal reasons, stating that “beating cancer two years ago”.
He said: “Beating cancer two years ago has led me to review what I want for the future. It has been the toughest decision of my life but I do feel that now is the time to move on.”