A graduate of the National School of Drama in Warsaw, he made his debut on stage in the play Szczęście Frania by Włodzimierz Perzyński. From 1955, he made many appearances in Warsaw Dramatic Theater. He made his screen debut in 1953, starring in the film Celuloza, under the directorship of Jerzy Kawalerowicz.
He would go on the star in another of Kawalerowicz's films, Shadow (Cień) in 1956, a film which was entered into the 1956 Cannes Film Festival. The film is a Rashōmon-like investigation into the life of a man found dead after having been hurled from a train.
Then in 1964. he starred in the Aleksander Ford film The First Day of Freedom, which was entered into the 1965 Cannes Film Festival. Kłosowski starred alongside Tadeusz Lomnicki, Beata Tyszkiewicz and Tadeusz Fijewski. In the late 1960s, he appeared in the World War II miniseries Czterej pancerni i pies.
In 1971, he appeared in the Polish superhero comedy film, Hydrozagadka, portraying the Maharaja of Kabur. The film was directed by Andrzej Kondratiuk.
From 1974 to 1976, he starred in the successful television comedy series Czterdziestolatek. From 1975 to 1981, he directed the Universal Theater in Łódź, and from 1981 worked at the Warsaw Mermaid Theater.
In 1986, he once again was directed by Andrzej Kondratiuk in the comedy-sci-fi television series Big Bang. Playing the character of Shepherd Kazimierz, he featured alongside actors such as Ludwik Benoit, Zofia Merle and Janusz Gajos. In 1989, he played the role of Edward in the Andrzej Barański's film, The Peddler. In 1996, he would again collaborate with Barański and appear in the psychological film, Dzień wielkiej ryby, in 1996.
Then in the 1990s, he starred in the Polish sitcom series Świat według Kiepskich. In 2008, he portrayed Nostradamus in the comedy drama film, Before Twilight (Jeszcze nie wieczór).
He ended his career in 2016 because of deteriorating health; he lost his sight after the operation.