Olshan was born in Kaunas in the Russian Empire (now Lithuania) in 1895 and immigrated to Ottoman Palestine in 1912.

As an attorney, he represented the Yishuv before the British Mandate of Palestine authorities.

He headed a parliamentary commission to investigate the Israel Defense Forces' (IDF) economy and the Central Elections Committee of the second Knesset.

[1] In 1954 he was appointed by Moshe Sharett head of the inquiry commission regarding the Lavon affair with President of the Technion and former IDF Chief of Staff, Yaakov Dori.

[2] In 1954, he succeeded Moshe Smoira as President of the Supreme Court.