Logan was part of a family of entertainers beginning with his parents who were the music hall act, Short and Dalziel. His aunt, from whom he took his stage surname, was Broadway star Ella Logan. His sister is actress and jazz singer Annie Ross, and his brother is vocalist Buddy Logan.

Educated at Gourock High School, Inverclyde, Logan left school at the age of 14. His family, in the 1930s and 1940s, toured the small music halls of Scotland and Northern Ireland. By 1944 he was in pantomime when he played the cat in Dick Whittington and His Cat. His connection with pantomime would continue throughout his life.

Jimmy Logan established himself in the forefront of Scottish show business, particularly with The Five Past Eight Show at the Alhambra Theatre, Glasgow. Logan purchased the Empress Theatre (located not far from St George's Cross) for £80,000 in 1964. He refurbished it at great personal cost, opening it as the 'New Metropole'. One of the first events to be staged there was the first Scottish production of the rock musical Hair. Further development was blocked by the planning authorities and spiralling costs almost ruined him. The theatre subsequently closed in 1972, and was eventually demolished.

His first acting role was in the film Floodtide (1949) which also featured Gordon Jackson, a drama set on Clydeside. He also performed in Carry on Abroad (1972) and Carry On Girls (1973), two of the long running Carry on series of films. His London stage debut came in The Mating Game (1973).

His adaptation of Oor Wullie, the Sunday Post comic strip character, for the Dundee stage was a failure, but his show Lauder (1976), a one-man musical based on the life of his hero, famed Scottish entertainer Sir Harry Lauder, proved a success. Logan's large collection of Lauder memorabilia now rests in the Scottish Theatre Archive at the University of Glasgow.

Other theatrical successes included The Entertainer (1984), Brighton Beach Memoirs (1989), Bill Bryden's The Ship, The Comedians (1991), On Golden Pond (1996) and Death of a Salesman at the Pitlochry Festival (1992). In 1991 he had a prominent supporting role in the popular Swedish comedy film Den ofrivillige golfaren, which was partly filmed in Scotland.

Logan was awarded an honorary doctorate by Glasgow Caledonian University (1994), honoured with an Order of the British Empire (OBE) for "services to Scottish theatre" in 1996, and was elected a Fellow of the Royal Scottish Academy of Music and Drama in 1998.

Logan's last two performances were at Pitlochry Festival Theatre and the Glasgow's Pavilion Theatre respectively.

Logan died before he ever saw his dream of a pantomime casted with his favoured football team, Partick Thistle take place.

Logan died of cancer in Clydebank, West Dunbartonshire, Scotland, 9 days after his 73rd birthday.