Other figures such as Rolf Harris, Simon Callow and Daley Thompson are also taking part in the TV experiment, which will form a Channel 4 documentary series next year.
Jamie's Dream School aims to encourage 20 teenagers who have had difficulties at school to give education a second chance.
Starkey will teach history, Lord Winston science and Campbell politics classes.
Oliver had difficulties at school, partly due to his dyslexia, and left at 16 with two GCSEs.
But the chef - who has already campaigned for healthy eating and improved school dinners - wants to see if others like him can succeed if they have the right environment.
He advertised in the summer to find youngsters who had failed to thrive in school. During the seven-part series, viewers will see if he can persuade the group, aged from 16 to 18, to try again with their education.
Oliver said: "What we're trying to do with Dream School is to provide loads of different academic subjects and some fantastic teachers so that there's something inspiring for all the young people, whether it's politics or history or sport or music.
"It's fascinating to watch the kids in different lessons and see what switches them on."