The death of the one-time chess prodigy was announced on Thursday by the International Chess Federation, the game's governing body. No cause was given.
Spassky was "one of the greatest players of all time," the group said on the social platform X. He "left an indelible mark on the game."
The televised 1972 match with Fischer, at the height of the Cold War, became an international sensation and became known as the "Match of the Century."
When Fischer won the international chess crown in Reykjavik, Iceland, the then-29-year-old chess genius from Brooklyn, New York, brought the US its first world chess title.
Fischer, known to be testy and difficult, died in 2008.
Former world champion Garry Kasparov wrote on X that Spassky "was never above befriending and mentoring the next generation, especially those of us who, like him, didn't fit comfortably into the Soviet machine."
Spassky emigrated to France in 1976.
On its website, the chess federation called Spassky's match with Fischer "one of the most iconic" in the history of the game.
Yugoslav grandmaster Svetozar Gligoric said that Spassky's secret strength "lay in his colossal skill in adapting himself to the different styles of his opponents," the Washington Post reported.
