Van Halen was part of the classic Van Halen line-up alongside his brother Alex, Michael Anthony on bass and David Lee Roth singing.
The band was hugely successful and has sold more than 80 million records worldwide.
In a statement shared on Twitter, Van Halen’s son, Wolfgang, said his father died on Tuesday.
He said: “I can’t believe I’m having to write this, but my father, Edward Lodewijk Van Halen, has lost his long and arduous battle with cancer this morning.
“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.”
Wolfgang, who became Van Halen’s bassist, added: “I love you so much, Pop.”
— Wolf Van Halen 🐺 🚐 🙌 (@WolfVanHalen) October 6, 2020