The deal came four days after the Rockets pulled off a stunning trade to acquire Harden from the Oklahoma City Thunder.
Houston traded shooting guard Kevin Martin and first-round draft pick Jeremy Lamb to Oklahoma City, along with future draft picks.
Rockets general manager Daryl Morey called Harden a "foundational player" on Monday, stating that the reigning Sixth Man of the Year is "a player we can build around."
The Rockets, who also signed point guard Jeremy Lin this offseason, visit the Detroit Pistons in their regular-season opener Wednesday.
