Moiseev was born in Moscow. He studied organic chemistry at Moscow State University of Fine Chemical Technologies (MITHT). After graduating in 1952, his first jobs were as an engineer, a junior researcher in physical chemistry, then a senior researcher in organic chemistry. From 1963, he worked at the N. S. Kurnakov  (IGIC) of the Russian Academy of Sciences (RAS), Moscow, as head of the laboratory of metal-complex catalysis and coordination chemistry. From 2003 onward, he was a professor at the Gubkin Russian State University of Oil and Gas (RGUNG Gubkin).
He also served as chairman of the Scientific Council for Gas Chemistry, RAS, and vice-president of the Russian Chemical Society.