He studied at the Slutsk gymnasium, but was expelled for participating in the Russian Revolution of 1905-1907.
In 1908 he was accepted to the mathematical faculty of Saint Petersburg University. In 1911, he was arrested for taking part in revolutionary riots and was imprisoned at Saint Petersburg and Pskov.
After his release in 1912, he re-entered the university and later transferred to the University of Tartu, from where he graduated with a degree in physics and mathematics.
After University, Ostrovskiy worked as a teacher in Częstochowa, Poland and in Minsk. From 1915 to 1917 he taught at the Minsk Teaching Institute. After the February Revolution of 1917 he became the commissar of the Provisional Government in Slutsk paviet. In September of the same year he founded the Slutsk Belarusian Gymnasium and became its principal. Ostrovskiy opposed the October Revolution of 1917. He was a delegate to the December 1917 First All-Belarusian Congress and published articles where he supported the idea of Belarusian independence. He took part in the 1920 Slutsk defence action against the Red Army.
In 1921, he moved into West Belarus in the Second Polish Republic. He served as principal of the Belarusian Vilnius Gymnasium from 1924 to 1936.
In the second half of the 1920s, he radically changed his political views. In 1924 he initiated the creation of a Polish-Belarusian Society that supported the Polish government. After the breakdown of the Society, Ostrovskiy cooperated with the Belarusian Communist Party (of Bolsheviks) and with the Communist Party of West Belarus, and managed the illegal komsomol cell in his gymnasium.
In 1925 and 1926 he was the vice-chairman of the Belarusian Peasants' and Workers' Union, the chairman of the Belarusian School Society, and the principal of the Belarusian Cooperation Bank in Vilnius. In 1926, Ostrovskiy joined the Communist Party of West Belarus and was arrested by the Polish police. However, during the trial against the Hramada he was found not guilty.
From 1928, he once again changed his political orientation and started to call for cooperation with Polish officials. For that he was condemned by many leaders of the Western Belarusian national movement.
In the mid-1930s he published various works in Belarusian calendar books and in the "Rodny Kraj" newspaper, under the pseudonym "Era". In 1936 he had to leave Vilno and moved to Łódź.
During the German occupation of 1939-1945, Ostrovskiy actively cooperated with German officials. In 1941 he moved to Minsk and worked in civil administration. He also created Belarusian administrations in Bryansk, Smolensk and Mahilyow and spent certain time as a Bürgermeister in all of those cities.
In 1943, Radoslav Ostrovskiy became the president of Belarusian Central Rada, a very limited national government, which the Nazis (who had begun to lose on the Eastern front) allowed to be created in order to gain some sympathy from the Belarusian population and therefore to be able to use them against the Soviet army.
Although the Rada did not have much real power, it was allowed to manage certain civil issues.
Ostrovskiy was one of the main organisers of the Second All-Belarusian Congress in 1944.
After the war, Ostrovskiy fled the Soviets and ended up in West Germany. In 1956, he moved to the United States. He actively participated in Belarusian national activism aboard, and was the main ideologist of the BCR as the legitimate Belarusian government in exile, thus not admitting such status for the Belarusian People's Republic Council.