The bill failed in the Senate two years ago. But Senate President Steve Sweeney, who didn't vote for it then and has regretted it since, is sponsoring the measure.
Democratic leaders in the Senate and Assembly will announce the bill's reintroduction Monday.
Gov. Chris Christie, a Republican, has said he's no fan of same-sex marriage. But gay rights activist Steven Goldstein says he wants to see the bill approved and sent to the governor, even if Christie's unlikely to sign it.
Democrats don't enjoy veto-proof majorities in either house. So Christie could ignore the bill if it reaches his desk, which would allow it to become law without his signature.
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