Ohmura was born in the Bunkyō ward of Tokyo in 1942. In 1965 he graduated with a B.Sc from the University of Tokyo and in 1969 received an M.Sc from McGill University. He later received a Dr.sc.nat from the ETH Zurich.
Ohmura is a professor emeritus of the Institute for Atmospheric and Climate Science at ETH Zurich, where he was the leader of the institute's climate research group. The group has strong interests in the planetary boundary layer and the cryosphere including its interaction with the atmosphere and ocean. The group maintains a general circulation model. Ohmura also initiated the Baseline Surface Radiation Network (BSRN).