Born in Billancourt, France, Souverbie studied art at the Academie Julian in 1910. Influenced by the Nabis painters, Souverbie enrolled at the Académie Ranson in 1916 where he befriended Bonnard, Vuillard and Vallotton. Souverbie developed a cubist style reminiscent of Georges Braque and Juan Gris' work. However, through his interest in balanced compositions, golden proportions and graceful distortions, he developed a unique style that was profoundly classical in character.
Souverbie's work matured during the 1920's following a meeting with Picasso in 1926 at the Vavin-Raspail Gallery in Paris. A year later, he was given a one-man-show at the same gallery, and in 1929, exhibited fifty-four paintings at the Galerie Bernheim-Jeune. In 1937, Souverbie was commissioned to paint the theatre in the Palais Chaillot. He later became the head teacher at the École des Beaux-Arts, at which an atelier for mural painting was created for him.
His first cubist works were exhibited at Bernheim Gallery in 1928. Inspired by ancient Greek figures and following a Cubist style, Souverbie's paintings of voluptuous nudes sensuously painted were well received and commissions for large murals soon followed. His monumental figures, his taste for allegorical subject matter and simplicity of composition reveals his interest in the great French classical painter, Poussin.
Souverbie's classicism does not only relate to seventeenth century tradition but equally to the laws of perfect beauty posed by the Greeks, and featured in the classical beauty of his young wife. It is her that is the model for the female figures in many of his paintings.
In 1925 Souverbie was under contract with the Galerie Vavin-Raspail, which hosted the Section d'Or exhibition that year, bringing him into contact with Lhote, Gleizes, Picasso, Marcoussis and many other members of the Paris avant-garde. After a first one-man-show at Vavin-Raspail in 1926 Souverbie went on to have a show of fifty-four cubist paintings at the Bernheim-Jeune Gallery in 1929, which established him as an important figure on the Paris inter war art scene. In 1935 he painted a decorative panel to represent France at The Brussels Exhibition, and three years later he designed the scenery for the Opera de Paris.
He was appointed head teacher at Ecole des Beaux-Arts in Paris (1945) and continued to paint, exhibiting his works mainly in France and Belgium. Between 1950 to 1975 he regularly showed his work at Chardun Gallery. In 1946 he was elected a member of the Academie des Beaux-Arts and an Officer of the Legion d'Honneur in 1950. His works are held in numerous public and private collections both nationally and internationally.