Nikolay Krasovsky was born in Yekaterinburg (renamed later to Sverdlovsk that year) in the family of a doctor.
In 1949, he graduated summa cum laude from the department of metallurgical science at the Ural State Technical University.
In 1954, he presented his first thesis and received his kandidat nauk degree in mathematics.
In 1957, he defended his second thesis for the degree of doktor nauk and became a professor of mathematics.
In 1963 Stanford University Press published a translation of his book Stability of Motion: applications of Lyapunov's second method to differential systems and equations with delay that had been prepared by Joel Lee Brenner.