The comedian made the announcement on Twitter, saying he did not want the alleged offensive posts to be a "distraction on the night".
According to reports, the tweets are more than a decade old.
Hart – who had previously described the gig as a "dream come true" – had earlier refused to apologise for the tweets, saying he had already addressed the issues.
But as the controversy continued to mount, the 39-year-old tweeted: "I have made the choice to step down from hosting this year's Oscar's….this is because I do not want to be a distraction on a night that should be celebrated by so many amazing talented artists.
"I sincerely apologise to the LGBTQ community for my insensitive words from my past."
"I'm sorry that I hurt people. I am evolving and want to continue to do so. My goal is to bring people together not tear us apart.
"Much love & appreciation to the Academy. I hope we can meet again."
Yesterday, he was defiant in the face of criticism posting an Instagram video the Academy had called him and requested he apologised.
He tells fans: “I chose to pass on the apology. The reason why I passed is because I’ve addressed this several times. This is not the first time this has come up. I’ve addressed it. I’ve spoken on it. I’ve said where the rights and wrongs were.”
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Hart reportedly deleted a number of homophobic messages — some of which were nearly a decade old — after getting picked to host the 2019 awards show on Tuesday.
When news organizations noticed what he did, they started reposting screen grabs of the messages, including one from 2011 that read: “Yo if my son comes home & try’s 2 play with my daughters doll house I’m going 2 break it over his head & say n my voice ‘stop that’s gay.”
Other tweets still live on Hart’s Twitter include messages like: “I just saw a n***** put a whole chicken wing in his mouth and pull it out with no meat on it!!!!!! God damn that was gay.”
GLAAD, the gay rights advocacy organization, wrote on Twitter that they reached out to Hart, ABC Network and the Oscars to discuss the tweets.
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