A source tells PEOPLE the Pirates of the Caribbean star "is totally devastated" after the English guitarist died at the age of 78 on Tuesday, noting that Depp, 59, "was by Jeff’s bedside" along with "some other rock stars" before Beck’s death.
"They had a really tight friendship, they were extremely close, and he got even closer over this past summer when they were touring together," the source shares. "The sickness came on really quickly and it all deteriorated rapidly in the last couple weeks."
"Johnny is still processing this news. He’s devastated," the source adds.
The duo also released an official music video for "This Is a Song for Miss Hedy Lamarr," the first single off the album.
"It’s an extraordinary honor to play and write music with Jeff, one of the true greats and someone I am now privileged enough to call my brother," the Sweeney Todd actor said in a release at the time.
Never miss a story — sign up for PEOPLE’s free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories.
"I haven’t had another creative partner like him for ages," Beck said of Depp at the time. "He was a major force on this record. I just hope people will take him seriously as a musician because it’s a hard thing for some people to accept that Johnny Depp can sing rock and roll."
The duo also performed several shows together.
Beck’s family confirmed his death in a statement to PEOPLE on Wednesday.
"On behalf of his family, it is with deep and profound sadness that we share the news of Jeff Beck’s Passing," the statement began. "After suddenly contracting bacterial meningitis, he peacefully passed away yesterday. His family asks for privacy while they process this tremendous loss."
RELATED VIDEO: Johnny Depp Performs for a Second Time in England Before Amber Heard Defamation Trial Verdict
Through the years, Beck — who rose to fame in 1965 when he took over as guitarist for The Yardbirds, replacing Eric Clapton — was featured in iconic moments in music from his role as lead guitarist on Mick Jagger‘s debut album She’s the Boss to the title track on Ozzy Osbourne‘s latest album titled Patient Number 9.
The eight-time Grammy winner is survived by his wife Sandra Beck.