Stewart Cochrane was born on October 25, 1933 in Dumfries, Scotland. The center forward started his career with St. Cuthbert Wanderers.
In 1957 Stewart joined Scottish League club Queen of the South. He played in one senior game for the Dumfries club. At the end of the season Stewart emigrated to Canada and arrived in Montreal in April 1958.
Stewart joined the Sparta club in Montreal and helped his new club to a seventh-place finish in the 1958 National Soccer League season. He finished the season as the second leading goalscorer in the NSL with 25 goals.
Before the start of the 1959 season the Sparta club was bought by new owners and changed its name to Canadian Alouettes. The club finished seventh in the final league standings in the 1959 National Soccer League season.
Stewart returned to Scotland in October 1959.