Neil Peart from the band Rush -- one of the greatest drummers in rock history -- died Tuesday after battling cancer ... according to his family.

Peart passed away in Santa Monica. The family says he'd been diagnosed with brain cancer 3 years ago, but hadn't announced it to Rush's legion of fans around the world.

The Canadian rock trio of Rush formed in 1968, but Neil didn't join his bandmates -- bassist Geddy Lee and guitarist Alex Lifeson -- until 1974. All 3 men were known as virtuoso musicians and Neil's solo's are legendary ... in particular his drumming on iconic songs like "Tom Sawyer."

His influence on today's rock musicians can't be overstated. If you, or your parents, were a drummer growing up in the 70s or 80s... you know about the endless hours amateurs spent trying to play like Neil.

Sadly, he announced his retirement from the band in 2015 -- he'd been battling chronic pain related to tendinitis. The following year they announced the band was done touring ... not only because of Neil's health, but Alex was also battling arthritis.

Geddy and Alex say if fans want to honor their "soul brother and bandmate" in some way ... please donate to a cancer charity in his name.

Rush was inducted into the Rock and Roll Hall of Fame in 2013.

Neil's first his first partner, Jacqueline Peart, with whom he had a common-law marriage, died from cancer in 1998. They'd been married for more than 20 years. He later remarried in 2000.

He's survived by Carrie Peart and their 10-year-old daughter. He was 67.