He was already a well-known conductor and composer in his native Poland and throughout Europe before he made his US debut in 1958, conducting The Cleveland Orchestra at the invitation of George Szell. He was music director of the Minnesota Orchestra from 1960 to 1979. He regularly lead major ensembles in Vienna, Berlin, Paris, London, Rome, Munich, and other European cities, and made frequent appearances with the most prestigious American orchestras, including those of Boston, Cleveland, and Philadelphia.
In 1968, he made his Salzburg Festival debut with the Wiener Philharmoniker. That same year, at the request of the late United Nations Secretary-General U Thant (2), he led the Minnesota Orchestra in a special concert in The General Assembly Hall Of The United Nations, commemorating the 20th anniversary of Human Rights Day. His debut at The Metropolitan Opera followed two years later, when he conducted performances of Mozart's "The Magic Flute" at the Lincoln Center Theater and also on a national tour.
Among his acclaimed compositions is the "Concerto for Clarinet and Orchestra", premiered by the Minnesota Orchestra under Skrowaczewski's own baton on April 1981.