Domkat Bali was born in Langtang, Plateau State to the family of Hassan Bali Tabut and Yinkat Bali. He had his primary education at Mban, Langtang and from 1955 to 1960, he attended the provincial secondary school at Kuru. He undertook further military courses at Camberley, London.
He entered Nigeria Military Training School, Zaria in 1961 and in 1964, he was a lieutenant and troop commander. Bali became captain a year later in 1965. In 1966, he was battery commander and during the Nigerian Civil War, he was a regimental commander. He was made major in 1968. Between 1970 and 1971, Bali was commander, Corps of Artillery and later became a colonel at the Second Infantry Division in Ibadan. In 1973, he was posted to Akure as the commander of the 9th Infantry Brigade, he was adjutant general Nigerian army in 1975, commander Corps of Artillery in 1976 and in 1978, he was the GOC of the First Infantry Division, Kaduna. Prior to becoming Defense Minister in 1984, he was commandant at the Staff College and later director of army training and operations.  He resigned from the army on January 10, 1990 after President Babangida took over his post as minister for defence. He was a board member of HFP Engineering, builders of Victoria Garden City and later took up farming as a hobby.