He began his playing career with Dundee United, where he made 140 league appearances and was part of the team that won the 1994 Scottish Cup final.
During that season, Welsh was part of the Scotland under-19 team who reached the semi-finals of the UEFA European Under-19 Championship, losing 1–0 to Italy.
Welsh became a regular in the United side in 1993–94 and helped the club win the Scottish Cup for the first time, particularly by scoring in the semi-final against Aberdeen.
[2] He claimed that an injection administered by Morrison had ruined his career,[2] and an out-of-court settlement for a "substantial sum" was reached.
[2] After his playing retirement he helped coach the Cowdenbeath squad before being appointed team manager in October 2006, succeeding Mixu Paatelainen.