The deal will feature a player option in the second year, sources said.
Gasol had emerged as the target of a lucrative free-agency bidding war that had also involved the Portland Trail Blazers, Minnesota Timberwolves and Toronto Raptors, sources said.
Hall of Famer David Robinson took to Twitter on Monday to welcome Gasol to the Spurs' "family."
Gasol, who will turn 36 on Wednesday, spent the past two season with the Chicago Bulls and gave the team a solid offensive punch down on the blocks and provided a professional presence in the locker room.
Last year he averaged 16.5 points and 11.0 rebounds for a Bulls team that missed out on the playoffs.
Information from ESPN's Nick Friedell was used in this report.