A talented winger, he joined a team that included Harry Hubbick, Nat Lofthouse, George Hunt, Jack Hurst, Tommy Sinclair, Malcolm Barras, Albert Geldard, Jack Atkinson, Stan Hanson, Ray Westwood, Tom Woodward, Jackie Roberts, Don Howe and Ernie Forrest.
In the 1945-46 season Bolton finished in 3rd place in the North League 1945-46 season. Moir scored 9 goals in 31 games.
Moir made his debut in the Football League against Chelsea at outside-left. However, at the beginning of the 1948-49 season, he was switched to inside-right and scored all four goals against Aston Villa. That season he ended up as top scorer with 25 goals, beating the regular title holder, Nat Lofthouse.
In the 1952-53 season Bolton Wanderers beat Notts County (1-0), Luton Town (1-0), Gateshead (1-0) and Everton (4-3) to reach the FA Cup final. Their opponents, Blackpool, was managed by Joe Smith, the hero of their 1923 FA Cup victory. Moir scored in the final but Bolton lost the game 4-3.
Moir scored 118 goals in 325 games before joining Stockport County in September 1955. He scored 26 in 70 before leaving the club in 1957.
Willie Moir died in 1988.