"In this conversation, @KevinHart4real was authentic and real, and I'm in his corner," she said.
During the interview with DeGeneres, who is openly gay and hosted the Oscars in 2014 and 2007, Hart apologised again for the tweets, but said he did not want the awards to be about his "tweets from 10 years ago and homophobia".
"I do not want to stand on that stage and make that night about me and my past, when you have got people who have worked hard to step on that stage for the first time and receive a reward."
He added: "Either my apology is accepted or it isn't. Either I can move forward as a person or I can't. But you can't grow as a person without mistakes.
"There is no perfect bone in my body. I have made mistakes and I have embraced them all because I am a better man today because of it. I want to be done with this conversation."
He added that he had apologised at the time, 10 years ago, for the tweets.
DeGeneres said: "I know you are not that guy because I know you. I think the night will be about you, and it should be about you, and you should host the Oscars, and I'm going to talk you into it."
Has Hart 'reached out'?
But Nick Levine, a UK journalist who writes about pop culture and LGBT issues, told the BBC: "Like Ellen DeGeneres, I believe in forgiveness and second chances, but I also believe those things need to be earned.
"Has Kevin Hart made any meaningful effort to reach out to the... community and listen to their perspective on why his past comments are so offensive and damaging?
"I think if he did that, he'd understand why things he said a long time ago - which he's apologised for, and I'm sure completely regrets - have caused him to lose this incredible global platform.
"Once he demonstrates a greater awareness of why his comments hurt... we can start talking about forgiveness and the possibility of Hart hosting the Oscars again."
Others have expressed a similar sentiment on social media.