Yegorov came from a medical background, with his father a prominent heart surgeon, and his mother an ophthalmologist. He also selected medicine as a career and graduated from the First Moscow Medical Institute in 1961. During the course of his studies, he had come into contact with Yuri Gagarin's training and had become interested in space medicine.
Yegorov was selected as a member of the multi-disciplinary team that flew on Voskhod 1. It has been suggested that his father's influence within the Politburo may have had some bearing on the selection.
He eventually earned a doctorate in medicine, with his specialisation being balance.
He was married three times and died from a heart attack.