The 6-foot-8 Harrell averaged 11.6 points and 6.9 rebounds in a three-year career at Louisville. This season he averaged 15.7 points and 9.2 rebounds — both career highs.
He helped Louisville to the round of eight in this year's NCAA tournament.
The Rockets selected Wisconsin forward Sam Dekker with the 18th overall pick in the draft earlier on Thursday night.
He joins a Houston team that advanced to the Western Conference finals for the first time since 1997 this season before being eliminated by eventual champion Golden State.