Abba Musa Rimi was born on 28th February 1940 Rimi in Katsina State. He attended Rimi Elementary School (1948-1951) before proceeding to Katsina Middle School in 1952. In 1953 he gained admission to Malumfashi Senior Secondary School and was a student of Kaduna Technical Secondary School (now Government College Kaduna) from (1955-1959).
On completion of his secondary school education, he worked for various organizations which include United African Company (UAC) as a Sales Representative (1960-1962); Nigeria Tobacco Company (NTC) as a Marketing Canvasser (1963-1965); United Bawo Construction Company as Administrative Secretary and later Administrative Manager, (1970-1978).
He was Deputy Governor of Kaduna State (Oct. 1979 to June 1981) before succeeding Alhaji Abdulkadir Balarabe Musa as Kaduna State Governor in June 1981 and served until September, 1983. His hobbies include watching films and reading.