The Spiders announced the signing of the 28-year old earlier today following his departure from Greenock Morton, another team once managed by McKinnon.
McHugh spent two seasons at the Falkirk Stadium from 2015 to 2017 where he made 63 appearances in all competitions and scored 11 goals.
He joined the Bairns following impressive performances as a tiralist in pre-season friendlies against Drogheda United and Athlone Town, scoring twice in both matches.
He most memorable moments in a Falkirk shirt came in the 2016 Scottish Premiership play-off semi final matches against Hibs where he netted a 90th minute equaliser at Easter Road to secure a 2-2 draw in the first leg and then a stoppage time winner at the Falkirk Stadium to make it 3-2 and send the Bairns in to the play-off final against Kilmarnock.
Prior to joining Peter Houston's side McHugh had eight years with his first club, Motherwell, but spent the final two on-loan at Queen of the South and Airdrieonians.