Terms of the deal weren't disclosed but Spurs general manager R.C. Buford said Thomas will be with the team at least two seasons.
"He was a big part of a team that went to the Western Conference finals [last season], and if we're going to pursue the championship Kurt will continue to be a big part of that," Buford said. "I don't know how long his career will go, but at least we know the next couple of years are going to be with us."
The 6-foot-9 Thomas, a 14-year veteran, was unavailable for comment.
Since being acquired from Seattle in a trade-deadline deal, he averaged 4.5 points and 4.9 rebounds for the Spurs in 28 games. He appeared in all 17 playoff games for San Antonio, averaging 4.1 points and 4.9 rebounds.
Thomas has also played for Miami, Dallas, New York and Phoenix. In 817 career games, he has averaged 9.7 points and 7.4 rebounds.
Horry, who has seven championship rings, will be 38 when the season begins. Finley, like Thomas, will turn 36 this season.
Buford would not comment on negotiations.
The Spurs already have signed free agent Roger Mason Jr. from the Washington Wizards. Mason, 6-5, is expected to be a backup guard. George Hill, the team's No. 1 draft choice this year from Indiana-Purdue-Indianapolis, is expected to add more depth at guard.
Besides Thomas, the Spurs are expecting 21-year-old Ian Mahinmi to get more minutes at forward. Mahinmi, the Spurs' first-round pick in 2005, played mostly with Austin of the NBA Developmental League, averaging 17.1 points and 8.2 rebounds per game.
The signing of Thomas was important considering Mahinmi's inexperience and the signing of a longterm contract in Spain by last year's top draft pick, 7-foot Tiago Splitter.
"He fits us at this time," Buford said. "He has great maturity and presence in the locker room, and winning a championship is important to him."