Stoudamire joined the team for practice after signing the contract, the San Antonio Express-News reported.
"This is a perfect situation to extend a career," he said after the workout.
Stoudamire's agent, Aaron Goodwin, told ESPN.com on Thursday that Stoudamire would sign for a pro-rated share of the $1.2 million veteran minimum. That computes to roughly $545,000 if Stoudamire spends the rest of the season with the defending champions.
Goodwin said Stoudamire, who cleared waivers and became a free agent Thursday after his buyout from the Memphis Grizzlies, committed to the Spurs after also considering the Phoenix Suns and Toronto Raptors, with whom Stoudamire won NBA Rookie of the Year honors in the 1995-96 season.
San Antonio had an immediate need for reinforcements in the backcourt.
Tony Parker was ordered last week by Spurs coach Gregg Popovich to sit indefinitely to rest a heel injury that, according to Popovich, had reduced the reigning NBA Finals MVP to "60 or 70 percent for about a month."
San Antonio will be hoping that Stoudamire's arrival will enable them to bring Parker back slowly, with the hope of getting him fully healed in time for the playoffs. The 34-year-old hasn't played in a game since Dec. 30, after Memphis made a commitment to give the bulk of its backcourt minutes to rookie Mike Conley and Spanish newcomer Juan Carlos Navarro.
Parker had wanted to play despite bone spurs in his heel, but Popovich said the injury is getting worse. An MRI exam showed Parker has chronic inflammation in the heel but no structural damage. The team said there still wasn't a timetable for his return.
The Spurs' Big Three of Parker, Manu Ginobili and Tim Duncan have all missed time with injuries during the first half of the season, contributing to a 12-13 slump since their 17-3 start that had dropped San Antonio to sixth in the West.
Stoudamire initially expressed strong interest in joining the Boston Celtics as a veteran counterpart to second-year playmaker Rajon Rondo, but it appeared the Celtics were banking on the future availability of Los Angeles Clippers guard Sam Cassell. It's widely expected that the Clippers will consent to buying out Cassell if they can't move him before the Feb. 21 trade deadline and Cassell remains close to this day with Celtics forward Kevin Garnett after their time together in Minnesota.
The Suns wanted Stoudamire -- who played collegiately in the area for Arizona -- as the reliable backup to Steve Nash they've been seeking for years. Stoudamire was also intrigued by the idea of playing behind Jose Calderon in a coming-full-circle return to the Raptors, who have been forced to look for a third point guard because of T.J. Ford's ongoing injury absence.
Marc Stein is the senior NBA writer for ESPN.com. To e-mail him, click here.