The 26-year-old averaged 5.5 points, 5.5 rebounds and 1.2 assists in 61 games last season with the New York Knicks.
Aldrich, 6 feet, 11 inches, was drafted by the New Orleans Hornets as the 11th pick in 2010. He has a career average of 3.1 points, 3.4 rebounds and 0.5 assist a game over 196 total games with the Oklahoma City Thunder, the Houston Rockets, the Sacramento Kings and the Knicks.
Aldrich will be playing behind Clippers' staring center DeAndre Jordan.
Follow Melissa Rohlin on Twitter @melissarohlin