He was born on May 9, 1882 in Bila Tserkva, Ukraine, the son of a long line of cantors.
Rosenblatt's devoutly religious upbringing prevented him from receiving formal musical training at any of the great academies of his day. He began his career as a member of the local synagogue choir. Quickly lauded as a child prodigy, Rosenblatt's solo career was launched.
He accepted his first full-time position in Munkacs, Hungary at the age of eighteen. Shortly afterword he relocated to Bratislava. He later occupied a position in Hamburg, Germany. In 1912 he moved to Harlem to take a position at the Ohab Tsedek orthodox congregation.
Rosenblatt's fame extended beyond the Jewish world earning him large concert fees, a singing role in the 1927 film The Jazz Singer, and the sobriquet "The Jewish Caruso".
He died on June 19, 1933 in Jerusalem.