He also said he will surrender his £67,060 salary as an MP, though he could also be legally forced to give up a large portion of his £143,911 mayoral salary if he joins the Commons.
The decision was orchestrated by Mr Cameron following years of rivalry between the two men.
However, Mr Johnson’s return to Parliament will pose a major challenge to George Osborne, the Chancellor, who is widely tipped to be planning a leadership bid when Mr Cameron stands aside.
Mr Johnson earlier this year clashed with Michael Gove, a key ally of Mr Osborne, after the former education secretary said that the Mayor would be “unfit to lead the nation”.
It could lead to a split in the Tory Party after the next election, with factions of MPs forming behind either Mr Osborne or Mr Johnson.
Theresa May, the Home Secretary, is also thought to be plotting a future run at the leadership.
Some insiders believe Mr Johnson’s return will destabilise Mr Cameron because it will lead to constant debate about whether the Mayor is attempting to unseat the Prime Minister.
“We have danced around it for an awfully long time now and, as you know, the Prime Minister has been clear that I can’t endlessly go on dodging these questions as I have tried to do so,” Mr Johnson said. “I have not got any particular seat lined up, but I think that in all probability I will try to find somewhere to stand in 2015.”
A Cabinet role, particularly in the business department, is seen by Mr Johnson’s allies as a key staging post in his bid to become Conservative leader once Mr Cameron steps down.
“Look at his record in London on transport and also on championing the city abroad,” one friend said. “Being a cheerleader for Britain as part of the Government and encouraging people to invest here is exactly the kind of thing he could do.”
Mr Johnson told the Telegraph: “I’ve got to deliver for London. I’ve got to fulfil the mandate and that’s got to take priority. Being in Westminster will actually be an advantage from the point of view of my job in London. I’ll be able to be an advocate for the city.”
Asked whether he would want a Cabinet post as Business Secretary, or a newly created role as infrastructure minister, Mr Johnson said: “Before any such discussion could take place there are still all these hoops I’ve got to go through. We’re still quite a long way off.”
Some Westminster insiders believe that if Mr Johnson is seen as an integral part of a Conservative victory next year, there could be an organised takeover in 2018 if Mr Cameron decides to step down.
However, one Cabinet minister said: “There will be no organised takeover in 2018 in Boris’s favour. He doesn’t have the support in the party and there’s a big object standing in his way in the shape of George Osborne.”
Mr Johnson repeatedly denied that he has any leadership ambitions. He said: “When David Cameron finally steps down, in 2030, or whenever, it may be that there’s a vacancy, but it will probably be filled by a person who’s a teenager now.” Mr Johnson’s announcement came after he delivered a fiercely Eurosceptic speech, saying Britain has “nothing to fear” if it leaves the EU.
Christopher Hope, The Telegraph’s senior political correspondent, questions Boris Johnson about the ministerial job he wants – and how much is a loaf of bread