Cameron said he was standing for election to serve for a full second term - which could last until 2020 - but joked: "Terms are like shredded wheat: two are wonderful but three might just be too many."
He named three of his senior colleagues - Home Secretary Theresa May, Chancellor George Osborne and London mayor Boris Johnson - as possible replacements as Conservative leader when he stands down.
In an interview with BBC News, Cameron was directly asked if he would go for a third term if he remained PM after the election. He replied: "No, I think I'm standing for a full second term."
And he added: "I'm not saying all prime ministers necessarily definitely go bad, or even go bad at the same rate, but I feel I've got more to bring to this job, the job is half done, the economy's turned round, the deficit is half down and I want to finish the job.
"I didn't just come to do this to, you know, deal with the debts and the mess, I want to go on with the education reforms and the welfare reforms.
"There definitely comes a time where a fresh pair of eyes and fresh leadership would be good, and the Conservative Party has got some great people coming up: the Theresa Mays, and the George Osbornes, and the Boris Johnsons. You know, there's plenty of talent there. I'm surrounded by very good people. The third term is not something I'm contemplating."
Cameron said political leaders should never regard themselves as "indispensable".
"Countries, like big organisations, benefit from strong and consistent leadership but there comes a time when you want a fresh pair of eyes and a fresh agenda," he said. "Certain things that other people would bring, and so you must never think that you're indispensable. However mad you go in this job.
"I've said I'll stand for a full second term, but I think after that it will be time for new leadership. Terms are like shredded wheat : two are wonderful but three might just be too many."
Cameron paid tribute to his wife Samantha for keeping him "sane" in Downing Street, and revealed she will be playing a role in the Conservative election campaign.
"The fact that we do different things helps actually," he said. "She keeps me sane because she's one of the most organised people that I've ever come across, so home life, the children's life, everything is just brilliantly organised.
"Otherwise you wouldn't get this family time - unless you're really well organised everything would be blown off course, you wouldn't get the chance. She's amazing like that.
"But we'll be out on the campaign trail because we're passionate about this election and what comes next. She is right behind me and what I'm trying to do."
He added: "She will be out there campaigning with me some of the time, she will be out there on her own supporting Conservative candidates some of the time, but she has also got a job and we've got three children."