Leonid Filatov was born on December 24, 1946, in Kazan, Tatarstan, Soviet Union (now Kazan, Tatarstan Russia). His father, Aleksei Eremeyevich Filatov, was a radio engineer who traveled frequently, and his parents divorced when he was 7 years old. Young Leonid Filatov moved with his mother, Klavdia Nikolaevna Filatova, to the city of Ashkhabad, Tadjikistan. There he made his stage acting debut in an amateur play at a secondary school. In 1965 he came to Moscow and applied to State Institute of Cinematography (VGIK), but failed the entrance exam. However, his persistence and determination soon paid off, and from 1965 - 1969 Filatov studied at Schukin Theatrical School at Vakhtangov theatre, graduating in 1969, as an actor.

From 1969 - 1985 and from 1987 - 1993 Filatov was a permanent member of the legendary troupe at Taganka Theatre under the leadership of director Yuriy Lyubimov. There his stage partners were Vladimir Vysotskiy, Valeriy Zolotukhin, Ivan Dykhovichnyy, Natalya Sayko, Boris Galkin, and Aleksandr Porokhovshchikov among other notable Russian actors. During 1985-1987 he worked with the troupe of Sovremennik Theatre in Moscow, then returned back to Taganka. In 1993 Filatov joined Nikolay Gubenko, Natalya Sayko, Zhanna Bolotova, and Nina Shatskaya in formation of an independent company called "Sodruzhestvo akterov Taganki" (aka.. Fraternity of actors from Taganka).

Leonid Filatov shot to fame with the leading role as Igor Skvortsov opposite Georgi Zhzhyonov and Alexandra Yakovleva in a popular Russian film Ekipazh (1980), by director Aleksandr Mitta. During the 1990s Filatov made a career as film director. From 1994 - 1997 he hosted a popular TV show on the Russian National TV, titled "Chtoby pomnili" (aka.. To be remembered). In 1997 Filatov suffered from a stroke, then had his kidneys removed, and remained bedridden for several years. He received thousands of letters from his fans and admirers. Filatov also was comforted by his beloved wife, Nina Shatskaya who cared for him during all seven years of his illness. At that time Filatov suffered from much physical and emotional pain, as well as from depression because he was unable to go back to acting, so he expressed himself through writing.

Leonid Filatov was designated People's Artist of Russia (1994). He was awarded the state Prize of Russia for his work in theatre and film. His books and plays were adapted to stage and film. Leonid Filatov died of pneumonia and complications from a kidney disease on October 26, 2003, in Moscow, Russia, and was laid to rest in Vagankovskoe Cemetery in Moscow, Russia.