After three seasons with Dundee United he came to the attention of West Ham United. Turning down an initial bid of £175,000 he transferred to West Ham for a fee of £430,000 in 1979 making him the most expensive teenage footballer at the time. Stewart made his West Ham debut on 4 September 1979, playing as a defender, in a League Cup game against Barnsley. His first West Ham goal, a penalty, came on 29 September 1979 in a 2–1 home win against Burnley. In 1980 West Ham won the FA Cup. Stewart was West Ham's top scorer playing a vital part in their victory, including two goals in the fourth round against Leyton Orient and a last minute penalty winner in the quarter-final against Aston Villa. In the semi-final replay on 16 April 1980, against Everton, Stewart was moved into central defence replacing an injured Alvin Martin. The following season Stewart was a vital member of the team which won the 1980–81 Football League Division Two, playing 41 games and scoring five goals, all penalties.