Wosner was born in Vienna, Austro-Hungary and studied in the Yeshivas Chachmei Lublin of Poland led by Rabbi Meir Shapiro. He was also a student of Rabbi Shimon of Zelicov who was the official supervisor at the Yeshiva. In Vienna, he had known and befriended the Rabbi Chanoch Dov Padwa of Galicia. He married and immigrated to Palestine before the Holocaust and settled in Jerusalem, where he studied at the Dushinsky yeshiva. It was in that time that, in spite of his young age, he became a member of the Edah HaChareidis. When he relocated to Bnei Brak, upon the incentive of the Chazon Ish, Rabbi Dov Berish Widenfeld of Tshebin, Rabbi Isser Zalman Meltzer, and Rabbi Yitzhak HaLevi Herzog, he established the Zichron Meir neighborhood and Yeshiva Chachmei Lublin, bearing the same name as the one in Lublin where he studied in his youth.