Squire announced last month that he had acute erythroid leukemia, a rare form of acute myeloid leukemia. He was receiving treatment before he died.
"It's with the heaviest of hearts and unbearable sadness that we must inform you of the passing of our dear friend and Yes co-founder, Chris Squire," said the statement from Alan White, Steve Howe, Jon Davison and Geoff Downes.
Squire was born on March 4, 1948, in London. He co-founded the band with its former lead singer, Jon Anderson, and the group released its self-titled debut album in 1969. Squire was the only member to play on all of Yes' albums.
"For the entirety of Yes' existence, Chris was the band's linchpin and, in so many ways, the glue that held it together over all these years," the band's statement read. "Because of his phenomenal bass-playing prowess, Chris influenced countless bassists around the world, including many of today's well-known artists."
Squire, a talented and dominant bass guitarist, was one of the leaders of progressive rock in the 1970s. His website says he was a choirboy in his youth, which set the foundation for his musical talents.
He released his solo debut, Fish Out of Water, in 1975, and also played in the short-lived supergroup XYZ (eX-Yes-Zeppelin), which included Jimmy Page.
Yes released the album Heaven & Earth last year. The Grammy-winning band's hits include "Roundabout" and "Owner of a Lonely Heart," which became a No. 1 hit on the Billboard pop charts in the 1980s. The group will launch a U.S. tour with Toto in August, when Billy Sherwood will fill in for Squire.
Squire is survived by his wife, Scotland, and several children.