After studying romance languages at the University of Berlin, he spent several years private tutor in Luckenwalde, Lyon and Sheffield because all the required recording in the Prussian school service was denied because of his political stance. After the First World War he joined the SPD and was mayor of the municipality Lankwitz, which was incorporated in 1920 in Berlin, later he was mayor of Finsterwalde in Lusatia. 1926 Ostrowski was elected for twelve years as mayor of Berlin -Prenzlauer Berg, but was dismissed in 1933 by the Nazis because of his Jewish wife. After the Second World War Ostrowski was mayor of Berlin -Wilmersdorf.
On December 5, 1946, he was elected mayor of Berlin. Ostrowski turned was against the forced merger of the Eastern SPD with the KPD to the SED, however, was more willing to cooperate with the SED. Through his good contacts with the Soviet commander he reached additional felling of the forests of the Soviet occupation zone in the hunger winter 1946/1947. As Ostrowski refused to dismiss the SED functionaries from the magistrate, made his own faction on April 11, 1947 a motion of censure against him, which was also adopted by a majority vote.
On April 17, 1947 Ostrowski resigned. His successor was on June 24, 1947 Ernst Reuter selected, but the office could not compete due to a Soviet veto. It was therefore incumbent Mayor Louise Schroeder. From 1948 to 1951 Ostrowski was president of the newly created main Berlin Examination Office.
Ostrowski died in June 1963 and was buried in the cemetery Wilmersdorf.