Kevin Burke was born in 1950 in London, England to parents from County Sligo in Ireland. He took up the fiddle at the age of eight, studied under Jessie Christopherson, and eventually acquired a virtuosic technique in the Sligo fiddling style. He travelled frequently to Ireland to visit relatives and immersed himself in the local Sligo music. By the age of thirteen, he was playing with Irish musical groups. He joined a céilí band, the Glenside, and played weekends at various Irish dance halls around London. In 1966, the Glenside performed at the céilí band competition at the All-Ireland Fleadh in Boyle in County Roscommon and won the competition.
In 1972, Burke met American singer-songwriter Arlo Guthrie in a pub in Milltown Malbay in County Clare. Impressed with Burke's fiddling, Guthrie invited him to Los Angeles to play on his album 'Last of the Brooklyn Cowboys' (1973). Burke's exposure to the musicians he met in the United States—including accordionist Joe Burke and fiddler Andy McGann—inspired him to devote his life to playing music. In 1974, Burke moved to Dublin, where he teamed up with singer-songwriter Christy Moore, a former member of the Irish band Planxty. Together with Jimmy Faulkner and Declan McNelis, they played throughout Ireland for the next few years.
In 1976, Burke became a member of the influential Irish traditional music group The Bothy Band. Burke replaced Tommy Peoples on fiddle, and soon became an integral member of the group, appearing on three of their albums: 'Old Hag You Have Killed Me' (1976), 'Out of the Wind – Into the Sun' (1977), and 'After Hours (Live in Paris)' (1979). Burke developed an especially strong musical bond with the band's guitarist and vocalist, Mícheál Ó Domhnaill, and soon the two began appearing together as a duo. When the Bothy Band disbanded in 1979, they toured the United Kingdom and Europe together, and recorded a highly acclaimed album, 'Promenade' (1979).
In 1980, Burke played the violin on Kate's song Violin.
In 1985, Burke joined the Legends of Irish Music tour, where he played with influential Irish musicians Andy Irvine (vocals, bouzouki, mandolin and harmonica) and Jackie Daly (accordion). Together they formed the group Patrick Street. During the next two decades, the group released nine albums and two compilations. In the early 1990s, Burke started touring and recording with Scottish fiddler Johnny Cunningham and Breton fiddler Christian Lemaître as the Celtic Fiddle Festival. Together they released six albums.
In 2002, Burke was awarded a National Heritage Fellowship from the National Endowment for the Arts, the highest honour given in the United States for folk and traditional music. In 2007, Burke started an independent record company, Loftus Music, to release his own recordings. Burke continues to tour around the world. He currently lives in Portland, Oregon with his wife and two children.