The Cheers and The Good Place actor, 78, revisited the incident during an appearance on Who's with Me?, a new podcast hosted by comedian and filmmaker W Kamau Bell, with their conversation partly focused on the performance Danson delivered while dating actress and comedian Whoopi Goldberg at the height of their relationship.
Danson's routine, which took place during a Friars Club roast honouring Goldberg, now 70, drew widespread condemnation after details emerged beyond the private event and remains one of the most controversial moments of the star's long career.
Danson said: "I would like to address this and apologise forever.
"I know what was in my heart. So, I have no problem talking about this, but I need to and want to apologise for the rest of my life because somebody today can go on the Internet, you're right, and go, 'What the f***? Wow. I feel betrayed. I feel angry and whatever'.
"And I did that."
Danson explained his blackface performance took place as his relationship with Goldberg was coming to an end and after the pair had unsuccessfully attempted to withdraw from the event.
He said: "So my brain was going, 'Okay, here is one of the most outrageous, funny, Black women in the world at that point. I'm supposed to be roasting her. And I'm not a stand-up. I can't run with the bulls'."
He said he eventually decided to approach the appearance as what he described as "performance theatre", before settling on an idea he now regards as fundamentally wrong.
Danson said: "I thought I could pull this off... (it was) so arrogant and stupid on my part."
The actor recalled the audience reaction inside the room quickly turned against him.
He said: "Twenty per cent of the crowd gets this and thinks it's pretty cool and gets it. Thirty per cent of the crowd gets it and f***ing hates it. Fifty per cent of the crowd didn't get it and f***ing hated it and hated me.
"And I kept going."
Danson also discussed the intense scrutiny he and Goldberg faced as an interracial couple during the early 1990s.
He said: "It couldn't be because they liked each other or saw something in each other.
"It had to be just pure sex, that's the only reason for a relationship like this."
According to Danson, criticism intensified almost immediately after the performance.
Goldberg publicly defended him at the time, telling The New York Times in 1993 the controversy "has caused great hurt to a man who doesn't deserve it".
However, Danson said her support did not lessen his responsibility.
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