Career
He joined Hibernian in 1996, where he spent three years, before ending his career with brief spells at Stenhousemuir, Clydebank and Cowdenbeath. He also represented the Scotland under-19 team Welsh returned to Cowdenbeath as manager from 2006 to 2008 and later became Head of Youth Development at Livingston, where he was also briefly caretaker manager.
He subsequently emigrated to the United States, where he is involved in youth coaching.
Welsh began his career with Dundee United, making his debut in the 1986-1987 season. During that season, in 1986, Welsh was part of the Scotland team who reached the semi-finals of the Union of European Football Associations European Under-19 Football Championship, losing 1–0 to Italy.
The following year, he reached the quarter-finals of the World Youth Championship, losing on penalties to West Germany. He then experienced relegation in 1995 and subsequent promotion with the club
Welsh scored a crucial goal in a promotion play-off match against Partick Thistle in 1996.
In August 1996 Welsh left Tannadice to join Hibernian in a £200,000 deal. Welsh was fined £300 after pleading guilty. Welsh began legal proceedings against Malcolm Morrison, who was employed as Hibernian club doctor during his time with the club, in 2008.
Welsh claimed that an injection administered by Morrison had ruined his career, and an out-of-court settlement for a "substantial sum" was reached.
After three years in Edinburgh, Welsh had spells with Stenhousemuir, Clydebank and finally Cowdenbeath, before retiring in 2002. After his playing retirement he helped coach the Cowdenbeath squad before being appointed team manager in October 2006, succeeding Mixu Paatelainen.
Welsh was sacked by Cowdenbeath in June 2008, following their relegation to the Third Division. The club stated that they had dismissed Welsh because he had incurred touchline bans due to misbehaviour during matches, but the judge ruled in his favour because the club had taken no action at the time and had dismissed him for unconnected reasons.
Welsh was appointed head of youth development by Livingston in July 2009.
He now lives in America and is Technical Director for Braddock Road Elite Travel Soccer of the Braddock Road Youth Club in Fairfax, Virginia.