Born in Calgary, Alberta, and raised on a farm in Erickson, near Creston, his childhood was somewhat isolated. After working as a farm hand, a bank clerk, and a park ranger, Birney went on to college to study chemical engineering but graduated with a degree in English. He studied at the University of British Columbia, University of Toronto, University of California, Berkeley and University of London.

Through a brief and quickly annulled marriage to Sylvia Johnston, he was introduced to Trotskyism. In the 1930s he was an active Trotskyist in Canada and Britain and was the leading figure in the Socialist Workers League but drifted away from the movement during World War II.

During the conflict, he served as a personnel officer in the Canadian Army, which was also the occupation of the title character of his comic military novel, Turvey (1949). The book has been described as "uproariously ribald", winning the Stephen Leacock Medal for Humour.

Birney published his second novel, Down the Long Table, in 1955.

In 1970 Birney was made an Officer of the Order of Canada.

In 1995 Birney died of a heart attack.