The 73-year-old, who performs with Depp in the rock band Hollywood Vampires, made the comments during a new interview with Page Six.
“Johnny is one of the sweetest people I’ve ever met in my life,” said Cooper.
“He is the most harmless human being I’ve ever met, so I’m not buying into all of the other stories because I know him and everybody else who knows him knows that.”
In March this year, Depp lost a bid to overturn a High Court ruling that concluded that he assaulted his ex-wife Amber Heard.
The Pirates of the Caribbean star had taken News Group Newspapers (NGN), which publishes The Sun, to court last year after an April 2018 column called Depp a “wife beater”.
The fallout from the legal proceedings led to Depp stepping away from his role as the villain, Gellert Grindelwald, in the forthcoming Harry Potter spin-off film Fantastic Beasts 3.
Casino Royale star Mads Mikkelsen is set to replace him in the role.
In the interview, Cooper added that despite Depp’s public persona, the actor is a “devout Christian”. He said that although the pair have not spoken recently, they have had email correspondence.
Cooper went on to commend his bandmate’s guitar skills, stating: “Johnny is a surprisingly good guitar player.”
Cooper, Depp and Aerosmith guitarist Joe Perry formed the rock band Hollywood Vampires in 2015.