The ex-Arsenal and Tottenham Hotspur defender said he could "bring something new to the table" as the Conservative nomination.
He said he wanted to "change London for everybody" but acknowledged he would not be a "frontrunner".
Campbell, 40, will take part in a hustings event with other candidates for the Tory nomination on 4 July.
Boris Johnson is planning to stand down as London Mayor in 2016.
Campbell, who also played for Portsmouth and Newcastle, told the Sun: "I'm going in with my eyes wide open. I know I'm not going to be a frontrunner.
"But I look at people who have been in politics for five, 10, 15 years, and muck up, you see them muck up and think, 'You guys are supposed to be pro!'
"People [who] have gone to Oxbridge, had thousands spent on their education, and I mean they are royally mucking up," he said.
Asked whether he could count on the votes of Spurs fans still bitter over his 2001 move to north London rivals Arsenal, Campbell said: "If we keep thinking about football, we're not going to do anything.
"We are dealing with people's lives here. I want to change London for everybody."
The Conservative Way Forward group confirmed that Campbell had signed up to take part in its mayoral hustings next month.
"We are delighted that candidates like Sol Campbell are throwing their hat in the ring and coming to debate the future of London at our hustings on 4 July," a spokesman said.
Also in the running for the Tory candidacy are entrepreneur Ivan Massow, current deputy mayor Stephen Greenhalgh and London Assembly member Andrew Boff, while MP Zac Goldsmith has also been tipped as a potential challenger.
Former England footballer Sol Campbell has confirmed his intention to become the next Mayor of London.