During the 2001 NBA draft, Terence Morris was chosen by Atlanta Hawks in the 2nd round. He was the 5th pick and overall 33rd pick. However, he was drafted to Houston Rockets immediately. He was associated with Columbus Riverdragons (Austin Toros) in the NBDL (NBA Development League) in the 2003-04 season. In September 2004, he made a deal with Los Angeles Clippers, but before the season began, he was waived. He became a member of Orlando Magic in September 2005. However, he was again waived in February 2006.
Then, Morris opted to move to Europe. He spent the 2004-05 season with Apollon Patras BC of the Greek League. At the start of the 2006-07 season, he was not affiliated to any team. He signed with Hapoel Jerusalem in December 2006. Along with this team, he won an Israeli State Cup championship. He was a member of Maccabi Tel Aviv during the 2007-08 season. Presently, he is a part of CSKA Moscow.
Terence Morris was with Houston Rockets during the 2001-02 to the 2002-03 seasons and with Orlando Magic during the 2005-06 season. He took part in 139 games and in these got the opportunity to play for 1934 minutes. His free throw percentage was 0.711, field goal percentage was 0.407 and 3-point field goal percentage was 0.196. He amassed 93 assists, 472 points, 377 rebounds and 126 personal fouls.