Dumbarton born inside forward Eddie Connelly started with Rosslyn Juniors in 1934 moving to Newcastle United for £90 in March 1935, for whom he made his debut in an FA Cup tie at Walsall in January 1936 scoring in a 2-0 victory. Described as “a clever ball manipulator”, he scored 9 goals in 22 matches as Newcastle finished 1935-36 in 8th position in the Second Division but he struggled to get a look in over the next two seasons and made only 8 further appearances before Luton Town bought him for £2,100 in March 1938.
He scored 16 goals in 51 appearances for The Hatters before being bought by West Bromwich Albion for £4,150 in August 1939 just before the suspension of peacetime football due to the onset of the Second World War. He scored once in 3 matches for Albion before the War for them and made 4 further appearances, scoring once, in their 1946 FA Cup campaign. During the War he guested for Blantyre Celtic, Dunfermline Athletic and Luton Town.
He returned to Luton Town for £2,000 in April 1946 scoring 8 goals in 39 further appearances for The Hatters before a move to Leyton Orient in June 1948. He scored 6 goals in 34 appearances during his year in East London joining Brighton & Hove Albion in October 1949 for whom he scored once in 7 appearances before a return to Scotland with Dumbarton in May 1950, leaving the club in October the same year before his retirement in February 1951.