Perry wrote Tuesday that he gave himself a few days to sit in the news of Beck's sudden passing before speaking on it publicly.
"No one, and I mean no one, played more lyrical guitar than Jeff Beck. He always had a bold insistence to play timeless melodies with simple emotional phrasing, like no other.
"My dream was that someday, I'd get to sing with him."
"His passing left a one of a kind voice that will never be filled!"
Perry closed by offering his condolences to Beck's family.
The singer's remembrance of Beck joins an outpouring of tributes from the likes of Jimmy Page, Paul McCartney, Mick Jagger, Ozzy Osbourne, Rod Stewart and many others.
Beck's family announced last Wednesday that the guitarist died peacefully the previous day, January 10, after a short battle with bacterial meningitis. They asked for privacy as they mourned.
Widely considered one of the greatest guitarists of all-time, Beck rose to prominence in the '60s as a member of the hitmaking British rock band, The Yardbirds.
After leaving the Yardbirds, Beck earned more acclaim with The Jeff Beck Group, whose early lineup featured a young Stewart on vocals. Though Beck would continue collaborating with singers through the years in various capacities, he cemented his legend as a solo artist who popularized instrumental rock music on the strength of his singular guitar prowess.