Born on 30 April 1899 at Geraldton, Western Australia, and registered as Asher Albert, he was the only son and second of four children to a Russian-born jeweller, and his English wife.
After serving articles in a legal firm, he was admitted to the Supreme Court on 20 October 1921, and practised at Goomalling and in Perth until appointed crown prosecutor in 1926.
In February 1959 he succeeded Sir John Dwyer as chief justice and became deputy president of the State Arbitration Court; he was knighted via KCMG in June.
He recommended improving literacy at the primary level, raising the school leaving age to 15, and reviewing policy and funding for technical education.
Sir Albert Wolff died on 27 October 1977 at the Home of Peace, Subiaco, and was buried in the Jewish Orthodox section of Karrakatta Cemetery after a State funeral.