Leigh made his debut for Livingston as a sixteen-year-old, after coming on as an 82nd minute sub, during a 3–1 defeat to Airdrie United on 30 December 2006. He went on trial at Premiership team West Brom in April 2009 and impressed enough to warrant a move. Fortunately for Griffiths & Dundee, a change of manager, with Tony Mowbray departing saw his chance of a move ended.

On 25 June 2009, Griffiths completed a £125,000 move to Dundee, despite having an offer rejected for the player back in April. He rejected contract talks with Hearts, citing the club's defensive playing style and his affiliation with rivals Hibs.

Leigh was selected for the Scotland B side that played Northern Ireland B at the end of the 2008–09 season, and he scored the third goal in a 3–0 win. He was a regular for Scotland at Under 19 level, and has since been selected to play for the Under 21 team. His first goal for Scotland U21 was on his second call up on 2/3/2010 where he equalised against Azerbaijan after being brought on as a substitution just a minute earlier.

On his arrival at Dens, it was clear his ambition matched that of the club when he declared "The SPL is where we want to be”.

Congratulations on your award, Leigh.