The state's Senate approved the measure by 19 votes to 4.

Hawaii's Democratic governor indicated he would sign the bill into law without delay. It is expected to come into effect on 2 December.

Same-sex marriages are currently legal in 14 US states and the District of Columbia.

Correspondents say the bill is likely to make Hawaii a popular wedding destination for same-sex couples.

Researchers at the University of Hawaii have said that the law will boost tourism income by $217m (£136m) over the next three years.

"I look forward to signing this significant piece of legislation, which provides marriage equity and fully recognises and protects religious freedoms," Governor Neil Abercrombie said on Tuesday.

US President Barack Obama welcomed Tuesday's vote, saying: "I've always been proud to have been born in Hawaii, and today's vote makes me even prouder."

Many credit a 1990 Hawaii case in which two women applied for a marriage licence with starting the whole nationwide debate on gay unions.

It led at least 30 other states to ban same-sex marriage and prompted Congress to pass the 1996 Defense of Marriage Act.

That law, defining marriage as between a man and a woman, was struck down by the US Supreme Court earlier this year.

Tuesday's vote in Hawaii adds to the momentum for gay marriage rights in the US.

Illinois senators passed a same-sex marriage bill earlier this month, and Governor Pat Quinn said he would sign it into law on 20 November.