According to a statement issued by Peart's family's spokesman, Elliot Mintz, Peart had been diagnosed with brain cancer.
Peart was widely considered one of the best drummers in rock history, with a flamboyant yet utterly precise style.
Born in Hamilton, Ont., Peart joined Rush in 1974, after the band's first album, replacing original drummer John Rutsey. Lifeson announced Rush's dissolution three years later.
Rush was inducted in the Rock & Roll Hall of Fame in 2013. "Then he sat down behind this kit and pummelled the drums - and us", Geddy Lee, the band's frontman, told the Guardian in 2018.
The Canadian band played a final tour in 2015 culminating in a final show at the Forum in Los Angeles.
He also wrote seven non-fiction books, including the memoir Traveling Music: Playing Back the Soundtrack to My Life and Times.
Peart leaves behind his wife, Carrie Nuttall, and daughter Olivia.
"I've been put in this position, and I certainly don't underrate that", he said.