The TV host, 49, has worked for the broadcaster for 13 years.
Jonathan was suspended in 2008 after leaving lewd messages on actor Andrew Sachs's answerphone with Russell Brand during a Radio 2 show.
He says his decision to go is not financially motivated.
'Over the last two weeks I have decided not to re-negotiate when my current contract comes to an end,' he says.
'I love making my Friday night talk show, my Saturday morning radio show and the Film Programme, and will miss them all.
'Working at the BBC has been a tremendous privilege, and I would like to thank everyone who has watched and listened so loyally over the last 13 years.'
Jonathan will remain working for the BBC until the summer and will continue hosting the Bafta Film Awards, Comic Relief and other BBC specials.