As a player, Houston played for Chelsea and Manchester United where he was a distinguished left back. He also played international football for Scotland.

Houston was assistant manager to George Graham at Arsenal from 1986, and was twice the club's caretaker-manager. first for three months in 1995 after George Graham's resignation in February 1995. Houston took his team to the final of the Cup Winners' Cup, but the Gunners lost to a spectacular last-minute goal from Nayim.

Arsenal appointed Bruce Rioch in the summer of 1995, but Houston remained on as his assistant. Just over a year after his appointment, Rioch was sacked, and Houston was reappointed as caretaker, while Rioch's designated successor, Arsène Wenger, waited to finish his contract at Grampus Eight. However, Houston didn't wait for Wenger's arrival, resigning his Arsenal post in mid-September to take over as manager of Queens Park Rangers, with Rioch becoming his assistant.

QPR, who had just been relegated to Division One, were aiming for a return to the Premiership, but Houston's spell at the club was not a success; he was sacked as manager in December 1997 with the club in the relegation zone. Houston was later reunited with George Graham when the latter became manager of Tottenham Hotspur in 1998, but left the club after Graham was sacked in March 2001. He has since spent a brief period as first-team coach of Walsall.