Stewart grows up in Dublin. He begins playing guitar when he is thirteen, influenced by guitarists Les Paul and Barney Kessel. He begins his professional career performing in Dublin showbands. In 1968 he wins an award as best soloist at the Montreux Jazz Festival. Soon after, he spends three years with Benny Goodman.
Stewart records his debut album, Louis the First, in Dublin, and then records in London with Billy Higgins, Peter Ind, Sam Jones, Red Mitchell, and Spike Robinson. From the mid to late 1970s he works with George Shearing, touring the United States, Brazil, and playing European festivals, and recording eight albums, including several in a trio with bassist Niels-Henning Orsted-Pedersen. He also appears on albums by Joe Williams and J. J. Johnson.
In 1981, ahead of his debut in the United States as a leader, The New York Times states, “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 states, “Louis Stewart is one of the all-time greats, and it is obvious from the first notes he plays on any occasion.”
Stewart receives an honorary doctorate from Trinity College, Dublin, in 1998. In 2009, he is elected to Aosdána, an Irish affiliation of people engaged in literature, music, and visual arts that was established by the Arts Council of Ireland in 1981 to honour those whose work has made an outstanding contribution to the creative arts in Ireland.