The new arrangement "eliminates any questions about two houses competing," said John S. Wisniewski, the Democrat who has spearheaded the Assembly's investigation.
Establishing the committee will require a new vote in the Legislature. Both houses voted unanimously last week to form the panels, but some Republicans have backtracked and accused Democrats of a partisan witch hunt.
It was unclear Tuesday whether the GOP would support the new effort; Democrats hold a majority in both houses. The bipartisan committee would include 12 members, eight from the Assembly and four senators.
"It's a good start," said Assembly Minority Leader Jon Bramnick (R., Union). "And now, hopefully, when we authorize action for the committee, they will do it on a bipartisan basis, as opposed to what was created in the Assembly committee."
On Friday, Assembly Democrats said they had served subpoenas to 20 people and organizations, including eight members of Christie's office.
Assembly Democrats previously rebuffed Sweeney's attempt to establish a joint committee.
On the Assembly floor Thursday, Majority Leader Louis D. Greenwald (D., Camden) told reluctant Republicans: "We are way ahead of where the Senate is. You want to slow this down? You think the people of Fort Lee want to slow this down so [the Senate] can catch up?"
Democrats would not say what had changed since then. Sweeney said he finalized negotiations with Assembly Speaker Vincent Prieto (D., Hudson) Tuesday morning.
The subpoenas seek documents about the September lane closures. Documents already obtained by legislators via subpoena and made public show the closures were orchestrated by Christie allies in an apparent plot to exact political retribution against the Democratic mayor of Fort Lee, possibly because he did not endorse the Republican governor for reelection.
Christie has denied involvement in or knowledge of the plot, and has said he was "embarrassed and humiliated" by some of his staff's behavior. The governor did not make reference to the controversy in his inaugural address Tuesday.
Earlier this month, Christie cut ties with two aides implicated in the scandal: his deputy chief of staff, Bridget Anne Kelly, and his former campaign manager, Bill Stepien. Two of the governor's appointees at the Port Authority of New York and New Jersey, which operates the bridge, resigned in December.
All four of those people have been issued subpoenas.