McKellar studied forestry at the University of Aberdeen, after graduation working for the Scottish Forestry Commission. He later trained at the Royal College of Music as an opera singer. He did not enjoy his time with the Carl Rosa Opera Company and left them to pursue a career singing traditional Scottish songs and other works. His albums of the songs of Robert Burns (now digitised) are considered by musicologists to be definitive interpretations.

In 1964 he toured New Zealand. On many occasions in the 1960s and 1970s he appeared on the BBC TV Hogmanay celebration programme, alongside Jimmy Shand and Andy Stewart. In 1966 BBC Television selected McKellar to represent the UK in the Eurovision Song Contest in Luxembourg. He sang five titles from which viewers selected "A Man Without Love" as the 1966 entry. According to author and historian John Kennedy O'Connor's The Eurovision Song Contest - The Official History, the Scottish tenor drew gasps from the audience when he appeared on stage. The song placed 9th of the 18 entries, making it the worst UK placing in the contest until the 1978 event. McKellar received scores from only two countries. Ironically, the Irish jury gave the UK song top marks, one of only two occasions the Irish have done so in Eurovision history.

On 31 December 1973, the first Scottish commercial radio station Radio Clyde began broadcasting to Glasgow. The first record they played was "Song of the Clyde" sung by Kenneth McKellar. The same recording features over the opening titles of the 1963 film Billy Liar.[citation needed]

McKellar made the majority of his recordings on the Decca Records label. He also recorded several classical works, including Handel's Messiah alongside Joan Sutherland in a performance conducted by Sir Adrian Boult

Kenneth McKellar died aged 82 a week after being diagnosed with pancreatic cancer. He passed away at the home of his daughter in Lake Tahoe in California.