The artist descended from a peasant family. His ancestors were Don Cossacks from Novocherkassk. He studied art in the Alma-Ata Teachers’ Training Institute and painting under the guidance of painter Zalzman, a student of Pavel Filonov. Begov taught at several educational institutions in Kazakhstan and Kyrgiziya. In 1983, he moved to Moscow being an accomplished artist. His solo exhibition held in the Tretyakov Gallery 1995 was marked as a significant event in Moscow cultural life. His parable paintings attracted general attention.

The next milestone in Alexey Begov’s artistic career was his solo exhibitions in European countries and America. The one held in Paris in 1997 had inordinate success. It was attended by Georges Mathieu, friend of Picasso and Dali, who was very complimentary about the works of the Russian artist. Soon, Alexey Begov received a large commission for painting St. Nickolas Chapel representing part of the Chateau de Gillevoisin architectural complex. To do the job, Alexey Begov with family spent several years in a small town of Janville. For his New Testament fresco series the artist received the highest award of the French Academic Society, the Art-Science-Literature gold medal. Alexey Begov returned to Russia having won recognition in the west. In June 2007, he was elected an Honorary Member of the Russian Academy of Arts. 

As of 2008, he shared his time between Moscow and Paris, worked hard and participated in prestigious exhibitions. In 2014, the artist passed away in Paris. The painting Snow and Umbrellas in Montmartre from the collection of the Kaluga Museum of fine Arts is one of his latest, crated in the last years of his life. In 2011, the painting was displayed at Begov’s solo exhibition in Kaluga and subsequently purchased from the author by the funds granted by the art and culture department of the Kaluga regional administration. In the painting, the artist depicted his family strolling along the Lavoisier street, in the vicinity of his studio.