Mamukelashvili tallied 14 points (4-5 FG, 3-4 3Pt, 3-4 FT), three rebounds, one assist and one steal in 18 minutes during Monday's 112-107 preseason loss to the Thunder.
The Spurs signed Mamukelashvili to a one-year, $2.2 million contract Tuesday, Adrian Wojnarowski of ESPN reports.
San Antonio renounced their free agent rights on Mamukelashvili on Monday, Keith Smith of Spotrac.com reports.
The Spurs extended a qualifying offer to Mamukelashvili on Sunday, Jeff Garcia of KENS 5 San Antonio reports.
Mamukelashvili posted 18 points (7-13 FG, 3-6 3Pt, 1-2 FT), eight rebounds and one assist over 26 minutes during Sunday's 123-95 win over Detroit.
Mamukelashvili totaled 21 points (8-14 FG, 3-5 3Pt, 2-4 FT), 12 rebounds, two assists and one block across 30 minutes during Friday's 121-120 victory over the Nuggets.
Mamukelashvili closed Tuesday's 102-87 win over the Grizzlies with 11 points (4-6 FG, 1-3 3Pt, 2-2 FT), 16 rebounds, four assists and one block in 26 minutes.
Mamukelashvili will join the starting lineup for Tuesday's game against Memphis.
Mamukelashvili will come off the bench during Sunday's game against the 76ers.
Mamukelashvili will start at power forward in Friday's game against the Pelicans, Paul Garcia of ProjectSpurs.com reports.