The Spurs swapped a future second-round pick for McCallum, whom San Antonio pegs as a replacement for the outgoing Cory Joseph.
The teams announced the deal Thursday.
Joseph came to terms on a new deal earlier this week with the Toronto Raptors.
Sacramento selected McCallum in the second round and 36th overall in 2013. He averaged 6.9 points, 2.7 assists and 20.7 minutes per game the past two seasons.
It was clear McCallum's time in California's capital city could be ending after the Kings reached agreement on a one-year, $10 million deal with Rajon Rondo last week. Rondo and Collison are expected to split time in the backcourt.
Information from The Associated Press was used in this report.