Jackson had become the highest-impact player available in the buyout marketplace and had been a target of the Clippers and Los Angeles Lakers.
Jackson, 29, will play a significant role on the Clippers' second unit, where coach Doc Rivers is anxious to implement his playmaking and scoring abilities into a roster that could be the NBA's deepest.
Jackson was completing the final season of a five-year, $80 million contract with the Pistons. The Pistons and Jackson's agent, Aaron Mintz of CAA Sports, completed the buyout terms earlier Tuesday before reaching an agreement with the Clippers on Tuesday afternoon.
Jackson has been a longtime friend with Clippers star Paul George and had long hoped to play with him, sources said.
Jackson has averaged 15 points and five assists in 14 games this season. He missed several weeks to start the season with a back injury that's now recovered.
In nine NBA seasons with the Oklahoma City Thunder and Pistons, he's averaged 12.9 points, 4.4 assists and 2.4 rebounds a game. Jackson was an outstanding performer in a backup role to Russell Westbrook and James Harden in Oklahoma City earlier in his career.
Jackson is expected to be one of the top free agent guards available in summer free agency.