Quadal was born at Niemtschitz (Czech: Němčice), near Kojetín in Moravia, in 1736. He came to London at an early age. He then studied painting and sculpture at the Akademie der bildenden Künste in Vienna and Paris Academy. He became a student of Francois Boucher in 1767. He was also employed by Louis Joseph, Prince de Conde and was particularly successful in France for his paintings of horses.
The painter visited France and Italy, worked at Vienna in 1787-9. He came to St. Petersburg in 1797 upon the invitation of Emperor Paul I and lived there until 1804. After a second visit to London, he returned to St. Petersburg, where he died in 1811.