The club was founded in 1901 and is named after Shamrock Avenue in Dublin, the place where the club was founded. They started playing friendly matches. In 1904/05 they began to play in a league. From 1907 till 1914 they were not allowed to play because they had no home ground. In 1921 they missed the founding of the league of Ireland, but the next season they played in this league and won the title. The next decades the Rovers were very successful. In 1967, they played as Boston Rovers one season in the United Soccer Association in the USA.