The Jazz sent the rights to last year's second-round pick Olivier Hanlan to the Spurs. Hanlan played this past season overseas.
The trade gives San Antonio enough cap space to sign Pau Gasol, who agreed to a two-year, $30-million deal with the Spurs on Sunday.
Diaw, a 13-year veteran, averaged 6.4 points, 3.1 rebounds and 2.3 assists per game last season with the Spurs.
Diaw, 34, will make $7 million this season. Utah will hold a team option for Diaw in 2017-18.