The bill, introduced by Del. James M. Scott (D-Fairfax), will result in council members shortening their four-year terms by six months during the transition.
It also dictates that candidates shall be nominated only by petition, and not by caucus, primary, convention or other party-affiliated proceeding.
A final House vote on the bill is expected Tuesday. If approved, it will head to the Senate.
Also, the Senate voted unanimously to pass a bill that would allow for staggered terms for the Fairfax County School Board beginning with the November 2015 general election upon a majority vote of its members. It still needs to be approved by the House.