Yegor was born as a son of Agafya Izotovna Zolotaryova and the merchant Ivan Vasilevich Zolotaryov in Saint Petersburg, Imperial Russia.
In December 1869, Zolotaryov defended his master's thesis “About the Solution of the Indefinite Equation of Third Degree x³ + Ay³ + A²z³ - 3Axyz = 1”.
In 1874, Zolotaryov become a member of the university staff as a lecturer and in the same year he defended his doctoral thesis “Theory of integer Complex Numbers with an Application to Integral Calculus”.
Starting at the beginning of the winter semester 1876 Zolotaryov was appointed extraordinary professor, and after the death of academician Somov he became his successor as an adjunct of the Academy of Sciences.
Yegor Ivanovich is not to be confused with the probabilist Vladimir Mikhaelovich Zolotaryov, Kolmogorov's disciple, who worked on stable distributions with well known results on their parametrization.