The U2 bassist credited guitarist Eric Clapton, The Who's Pete Townshend and his U2 bandmates for helping him kick his alcohol addiction.
The event, for the MusiCares Foundation, took place at New York's PlayStation Theatre, with performances from the likes of Macy Gray, The Lumineers, Jack Garratt and U2 themselves.
In a statement before the event, Adam said: "MusiCares does such vital work in helping vulnerable people across our industry. I know from experience the importance of an accessible, supportive environment in times of need and I'm always happy to do what I can to benefit this important organisation. I'm very much looking forward to the event."
Clayton's confessed his battle with his inner demons during an interview with Hot Press back in 2013, but on Monday, as he received an award from MusiCares - a foundation that helps musicians get treatment for addition - the bassist thanked Pete Townsend and Eric Clapton, as well as his fellow U2 stars, for advising him to stop drinking and helping him along the recovery process.
Taking to the stage, the 57-year-old U2 star joked: "I'm not used to achieving anything on my own."
He then talked seriously about his addiction. "I'm an alcoholic, addict, but in some ways that devastating disease is what drove me towards this wonderful life I now have. It's just that I couldn't take my friend alcohol. At some point I had to leave it behind and claim my full potential."
Clayton admitted that he thought his life as a rock star would be over if he gave up drinking as so much of the band's lives revolved around the night.
"But two heroes of mine were there for me and it meant a great deal that they would try to convince me otherwise," he said.
"After two particularly destructive benders Eric Clapton was there on the end of the phone. He didn't sugar-coat it, he told me that I needed to change my life and that I wouldn't regret it.
"He gave me the name of a treatment centre and the power to make a call to them. And whilst I was going through that five-week programme, Pete Townshend visited me and again put steel on my back."
"I was lucky because I had three friends who could see what was going on and who loved me enough to take up the slack of my failings.
"Bono, The Edge and Larry (Mullen Jr) truly supported me before and after I entered recovery and I am unreservedly grateful for their friendship, understanding and support."
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