Francis Clarke was the son of Sir William John Clarke, who had represented Southern Province in the Legislative Council between 1878 and 1897. He was born in Sunbury and educated in Melbourne and England. Initially he was a farmer, growing potatoes and onions at Port Fairy, then a pastoralist owning sheep stations at Deniliquin and Murchison. Eventually he moved away from the land and became a director of several companies, including the Colonial Bank, later the National Bank of Australasia. He married Nina Ellis Cotton in 1901.

Clarke was elected to the Legislative Council in 1913 as a non-Labor member. He represented Northern Province until 1925, Melbourne South Province between 1925 and 1937, and Monash Province from 1937 until his death in 1955, and was identified successively with the Nationalists, the United Australia Party, the Liberals, and the Liberal Country Party. He was Minister of Lands and Water Supply in 1918-21, and minister of Public Works in 1917-18, Minister of Water Supply in 1918-21 and Minister of Public Works in 1919-23. In 1923 he became President of the Legislative Council a position which he held until 1943. He was knighted in 1926.

In 1947, when he was again a backbencher, Clarke was instrumental in the denial of supply to the Cain government in the Legislative Council, an event which led to the government's electoral defeat in November 1947. As well as his father, Clarke's grandfather and two of his brothers were members of the Legislative Council. He died at South Yarra, and was survived by four children, his wife having predeceased him.