Eddie died from cancer on Tuesday, with his son, Van Halen bassist Wolfgang, announcing news of his death with a statement on Twitter.
Since then, figures from across the music world have been paying tribute to Eddie, who was a member of one of the world’s biggest rock bands during the 1980s.
David Lee Roth, Eddie’s former bandmate, posted a short message alongside a black-and-white picture of the pair together.
“What a Long Great Trip It’s Been..” David said.
The Who’s Pete Townshend told Rolling Stone: “It’s completely tragic that we have lost him.
“He was not just an innovative and stylish player with great taste, he was also a laidback virtuoso showman who just blew us all away every time.
“Every shredder today has lost their Master Teacher and Guide.”
Pearl Jam’s Mike McCready said he started playing guitar about a year after Van Halen’s 1978 self-titled debut album was released, saying it sounded like the late musician was “from another planet”.
He added: “Eddie was like Mozart for guitar. Changed everything and he played with soul.”
Sammy Hagar, a former Van Halen frontman who departed the band under acrimonious circumstances, shared a picture of him and the guitarist together.
He said: “Heartbroken and speechless. My love to the family.”
Lenny Kravitz described Eddie as “legendary” and a “musical innovator”.
Many other artists also paid their respects on social media...
Announcing Eddie’s death on Twitter, his son Wolfgang said: “He was the best father I could ever ask for. Every moment I’ve shared with him on and off stage was a gift.
“My heart is broken and I don’t think I’ll ever fully recover from this loss.”
Valerie Bertinelli, Eddie’s first wife and Wolfgang’s mother, later revealed she was at his side when he died.
Eddie first received treatment for tongue cancer in 2000 and the subsequent surgery removed about a third of his tongue.
He was declared cancer-free in 2002. It was reported last year that he had been privately receiving treatment for throat cancer for five years.