Born in Waterford, Ireland, Stewart grew up in Dublin. He began playing guitar when he was thirteen, influenced by guitarists Les Paul and Barney Kessel. Stewart began his professional career performing in Dublin showbands. In 1968 he won an award as best soloist at the Montreux Jazz Festival. Soon after, he spent three years with Benny Goodman.

Stewart recorded his debut album, Louis the First in Dublin, and then, subsequently in London, albums with Billy Higgins, Peter Ind, Sam Jones, Red Mitchell, and Spike Robinson. From the mid to late 1970s he worked George Shearing, touring America, Brazil, and major European festivals, and recording eight albums, including several in trio with Bassist Niels-Henning Orsted-Pedersen. He has appeared on albums by Joe Williams and J. J. Johnson.

In 1981, ahead of his debut in the US as a leader, The New York Times stated, "Mr. Stewart seems to have his musical roots in be-bop. He leans toward material associated with Charlie Parker and he spins out single-note lines that flow with an unhurried grace, colored by sudden bright, lively chorded phrases. His up-tempo virtuosity is balanced by a laid-back approach to ballads, which catches the mood of the piece without sacrificing the rhythmic emphasis that keeps it moving." In a review of Stewart's 1995 album Overdrive, AllMusic stated, "Louis Stewart is one of the all-time greats, and it is obvious from the first notes he plays on any occasion".

Stewart received an honorary doctorate from Trinity College, Dublin, in 1998. In 2009, he was elected to Aosdána, an Irish affiliation of artists engaged in literature, music and visual arts, established by the Irish Arts Council in 1981 to honour those whose work has made an outstanding contribution to the creative arts in Ireland.