The musician, considered one of rock’s greatest ever drummers, died on Tuesday in Santa Monica, California.
Rush, the band he played with for 45 years, confirmed his death in a statement posted to Twitter.
The statement said Peart, their “soul brother”, had been suffering from glioblastoma – a type of brain cancer – for three-and-a-half years.
“It is with broken hearts and the deepest sadness that we must share the terrible news that on Tuesday our friend, soul brother and band mate of over 45 years, Neil, has lost his incredibly brave three-and-a-half-year battle with brain cancer,” the statement says.
A spokesperson for the Peart family also confirmed the drummer’s death to US music magazine, Rolling Stone.
Placed at number four in Rolling Stone’s list of all-time greatest drummers, Peart was well-known for his technical proficiency and animated live performances.
He joined Rush in 1974, drawing influences from hard rock, jazz and heavy metal in a career that spanned four decades.
Peart retired from Rush in 2015 after the band’s final tour, saying the time had come to take himself “out of the game”.
The group, which also featured singer-bassist Geddy Lee and guitarist Alex Lifeson, recorded hits including The Spirit Of Radio and Tom Sawyer. The band was inducted into the Rock and Roll Hall of Fame in 2013.
Peart is reportedly survived by his wife, photographer Carrie Nuttall, and daughter Olivia.
Musicians have paid tribute to Peart on Twitter. Among them was Kiss frontman Gene Simmons, who described Peart as a “kind soul”.
He added: “My prayers and condolences to the Peart family, fans and friends.”
Actor and Tenacious D musician Jack Black tweeted: “The master will be missed – Neil Peart RIP.”