Voronin trained at Dynamo in Moscow, becoming the Honoured Master of Sports of the USSR in 1966. He became 1966 World Champion in the all-around and at rings. Participating in European Championships in 1967, 1969 and 1971, he became a champion in the all-around (1967, 1969), at rings (1967, 1969, 1971), on parallel bars (1967, 1969) and on pommel horse in 1967, winning 15 medals in total.
At the national level Voronin won the USSR Championships in the all-around (1968–69, 1970–71), at rings (1966–67, 1969–72), on pommel horse (1967, 1969–70), on parallel bars (1967, 1969), on high bar (1971) and in free exercise (1966).
After the 1972 Olympics he retired from competitions. Between 1973 and 1994 was the head coach, and then in 1994–2004 the president, of gymnastics club at Dynamo Moscow. Between 1978 and 1988 he was also president of the Russian Gymnastics Federation.
He was awarded the Order of the Red Banner of Labour in 1969, and became the Honoured Trainer of the Russian SFSR in 1979 and the Honoured Trainer of the USSR in 1980. In 1973 he graduated from the State Central Order of Lenin Institute of Physical Culture (GTsOLIFK).
His first wife Zinaida Voronina and son Dmitry Voronin were also competitive gymnasts. Mikhail and Zinaida divorced in 1980.