NBA front-office sources told ESPN.com on Friday that Finley and the Spurs have reached terms on a new deal that has been submitted for league approval.
Sources say the two-time All-Star also drew strong interest from the Hornets and Cleveland Cavaliers.
The Spurs, though, were determined to keep Finley, 35, even after signing swingman Roger Mason away from the Washington Wizards last month, with Brent Barry leaving San Antonio's wing rotation to sign with the Houston Rockets.
Heading into his 14th season, Finley joined the Spurs in the summer of 2005 after being waived by the Dallas Mavericks via the league's one-time amnesty provision, which allowed the Mavs to avoid paying a dollar-for-dollar luxury tax on the $51.8 million they owed Finley over the past three seasons.
The Spurs were eliminated by the Mavericks in a memorable second-round series in Finley's first season in San Antonio before winning the championship in 2007 to end Finley's decade-plus chase for a ring.
Finley then started 61 games last season for the Spurs, averaging 10.1 points and shooting 37 percent from 3-point range.
Marc Stein is the senior NBA writer for ESPN.com. To e-mail him, click here.