The upper house bill will now be debated in the House of Representatives, where if approved it will become law.
It follows a historic national vote that showed a majority of Australians support changing the Marriage Act.
Senators passed the bill 43-12 on Wednesday, after rejecting proposed amendments by conservative lawmakers.
Attorney-General George Brandis, the government's Senate leader, said the legislation would "demolish the last significant bastion of legal discrimination" concerning sexuality.
