Yegorov came from a medical family and trained as a physician in Moscow before specializing in space medicine and disorders of balance. His medical background matched the Soviet goal of flying more than military pilots on the new Voskhod spacecraft.

On October 12, 1964, Yegorov launched with Vladimir Komarov and Konstantin Feoktistov. Voskhod 1 carried three crew members without spacesuits because the modified spacecraft had to make room for the larger crew.

During the flight, Yegorov monitored crew health and carried out biomedical observations. He did not remain in the active cosmonaut corps long-term, but his single flight marked the beginning of physician-scientist participation in human spaceflight.