In 1959 he graduated from the Department of Mechanics and Mathematics of the Ural State University.
From 1970 to 1993 he worked at the Institute of Mathematics and Mechanics of the Ural Branch of the Academy of Sciences of the Soviet Union (later, of the Russian Academy of Sciences) in Yekaterinburg (from 1986 to 1993 he was the chief of the Institute).
In 1984 he was elected corresponding member and in 1987, full member of the Academy of Sciences of the Soviet Union (Division of Machine Engineering, Mechanics and Control Processes Problems).
Since 1993 Osipov has also served as the director of the V. A. Steklov Mathematical Institute in Moscow.
He holds a concurrent appointment as a professor of the Moscow State University.