Henry said he wanted to give the opportunity to play the character to a black actor.
“It’s been an honour to play Cleveland on Family Guy for 20 years,” he tweeted this week.
“I love this character, but persons of colour should play characters of colour. Therefore, I will be stepping down from the role.”
Henry, a white actor and comedian, has voiced Cleveland since Family Guy’s inception in 1999.
He also appeared the character on spin-off series The Cleveland Show, adding to a total of more than 300 performances across two series.
Family Guy creator Seth McFarlane retweeted Henry’s announcement without a comment of his own.
Henry’s decision coincides with The Simpsons’ announcement that white actors will no longer voice non-white characters on the show.
Hank Azaria, who has voiced controversial character Apu since his inception in the Nineties, previously revealed that he would no longer play the role.
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