Grechko graduated from the Leningrad Institute of Mechanics with a doctorate in mathematics. He went on to work at Sergei Korolev's design bureau and from there was selected for cosmonaut training for the Soviet moon programme. When that program was cancelled, he went on to work on the Salyut space stations.
Georgi Mikhailovich Grechko made the first spacewalk in an Orlan space suit. This spacewalk was made on December 20, 1977 during the Salyut 6 EO-1 mission.
He resigned from the space programme in 1992 to lecture in atmospheric physics at the Russian Academy of Sciences.
A minor planet 3148 Grechko discovered by Soviet astronomer Nikolai Stepanovich Chernykh in 1979 is named after him.