Campbell, who will take part in an event alongside other candidates for the Tory nomination on July 4, said he wants to "change London for everybody".
The footballer, who also played for Portsmouth and Newcastle in his top-flight career, 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 that have gone to Oxbridge, had thousands spent on their education, and I mean they are royally mucking up."
He added: "I bring something new to the table. This is a whole new road for me, something I can get my teeth into, but I just felt it was something I had to do.
"I come from a working-class background, it wasn't easy for me at all, but I worked hard. And now it's about giving something back."