'Flashing Lights' rapper Kanye made the apology as his open and emotionally-filled interview with Zane Lowe aired on BBC Radio 1 yesterday evening.
Taking to Twitter, Kanye said: "I would like to publicly apologise to Beck, I'm sorry Beck."
During his interview with presenter and producer Zane, Kanye was asked about that Grammy moment when he jokingly stormed the stage as Beck went to pick up his Best Album gong.
"I misconstrued it [the situation] but everybody has the right to an opinion," said Kanye. "Everybody has the right to be wrong. I expressed my opinion and I take the weight of it."
Talking about his changed opinion of Beck, Kanye continued: "As I was ironically having dinner with Taylor Swift, the Beck song starts playing and I was like, 'Wow, this is really good, maybe I might have been wrong.'"
I would like to publicly apologise to Beck, I'm sorry Beck.— KANYE WEST (@kanyewest) February 26, 2015
Kanye, who is married to US reality star Kim Kardashian, also apologised to Bruno Mars via Twitter last night, and asked the popstar to collaborate with him on a single.
Kanye had made comments about Bruno back in 2013, but now he wants to make amends.
Kanye tweeted: "I also want to publicly apologise to Bruno Mars, I used to hate on him but I really respect what he does as an artist.
"I also would love for Bruno to sing this hook on this song '88 Keys' Puff and I produced… I even asked Tyler to shoot the vid."
During Kanye's radio interview last night, the 37-year-old broke down in tears as he talked about the passing of fashion mentor Louise Wilson, who was a professor of fashion at Central Saint Martins College of Arts and Design in London.
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Watch Kanye's interview below - warning: this video contains strong language.