The legislation was expected to pass the final hurdle at the Scottish Parliament, the Scotsman has reported.
The vote on Thursday regarded the legal framework, which will pave the way for technical issues, such as the management and maintenance of the new crossing and the existing road bridge.
The Forth Estuary Transport Authority will be dissolved and its functions and assets will be transferred to the Scottish Government.
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All employees will transfer to the company appointed to operate the bridge.
The hearing comes just two weeks before a competition ends to name the new structure. To find a name, the Scottish Government launched a public consultation and eventually narrowed more than 7,000 suggestions to a shortlist of five.
The five choices are:
- Caledonia Bridge
- Firth of Forth Crossing
- St Margaret's Crossing
- Queensferry Crossing
- Saltire Crossing
Speaking about the idea behind the competition, Transport Minister Keith Brown said: "Other countries have been showing an interest in the way we are engaging the people of Scotland in the search for a name for the Forth replacement crossing.
"The response from the public has been tremendous, with over 27,000 people having voted so far."
The new crossing is expected to be completed in 2016.
(JP/CD)
