In a statement, Bowie remembered him as "a wonderful musician" who had been "a major inspiration for whichever band he was working with".
His death was announced by rock band Uriah Heep, who called him "a world-class bass player".
Bolder, who joined the band in 1976, stopped playing with them a few months ago due to poor health.
"Trevor was an all-time great, one of the outstanding musicians of his generation and one of the finest and most influential bass players that Britain ever produced," Uriah Heep said in a statement.
Spandau Ballet guitarist Gary Kemp also paid tribute on Twitter, writing: "RIP another Spider from Mars, a kind and decent man, Trevor Bolder. Love and peace to his family."
Bolder, who was born in Hull, East Yorkshire on 9 June 1950, joined his first band, Ronno, with guitarist Mick Ronson in 1970 after meeting on the local music scene.
He joined Bowie in 1971 to play on his fourth album, Hunky Dory, along with Ronson and drummer Woody Woodmansey.
This paved the way for 1972's The Rise and Fall of Ziggy Stardust and the Spiders from Mars, which launched Bowie and his bandmates into international stardom.
They played together on the albums Aladdin Sane and Pin-Ups before Bowie separated from the Spiders From Mars and moved to the US.
Bolder went on to join Uriah Heep, making his first appearance on their 1977 album Firefly.
Ronson died in April 1993, also of cancer, at the age of 46.
Trevor Bolder, bassist in David Bowie's 1970s backing band Spiders From Mars, has died from cancer at the age of 62.