The Edinburgh Wolves were originally formed in 2002 by a group of eight people who had previously played flag football. The Wolves name was adapted from the flag team that was absorbed into the organisation at the same time.

The club expanded and was accepted into the British Senior League (BSL) in November 2002. The League was rebranded to the British American Football League (BAFL) in 2005. The club moved to the BAFA Community League in 2010 after BAFL went into administration.

The club competed in the BSL in 2003, then the BAFL in 2003, 2004 and 2005 seasons. In 2006, due to a lack of linemen, the club were forced to pull out of the league. However, the club were able to play three games, including their first match at Meadowbank Stadium. The club returned to the BAFL in 2007, playing home fixtures at Meadowbank Stadium that season.

THe club competed in the BAFL Division 2 North until 2012. Following their first placed finish in the 2012 season, the club were promoted to the BAFL National League North for the 2013 season. The club finished second in the BAFL National League North division in 2013 and went on to become runners-up in that season’s Britbowl.
In 2019 the club competed in the British American Football Association’s Adult Premier League North division, finishing fourth.