The Spurs ultimately eliminated the Timberwolves in a six-game second-round series, prompting Minnesota to adjust its roster configuration.
The multi-team deal also sends center Nic Claxton to the Chicago Bulls, who absorb the remaining two years of his four-year, $97 million contract.
Chicago did not give up any assets to acquire Claxton, as reported by ESPN.
Claxton averaged 11.7 points, 6.9 rebounds, and 3.7 assists in 69 games this past season.
The 27-year-old center previously finished ninth in the Defensive Player of the Year voting during the 2022-23 NBA season.
Following the trade, the Brooklyn Nets now control two first-round draft selections, holding the No. 6 and No. 28 picks.
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Meanwhile, the Timberwolves enter Tuesday's draft possessing the newly acquired second-round pick from Brooklyn.