It will begin with establishing an advisory panel made up of independent civic, business and community representatives from across Scotland, who will responsible for gathering and assessing suggestions from members of the public.
All potential options will be considered by the panel before a shortlist of the most appropriate names is produced and put to a public vote to find the most popular.
It is anticipated that the public vote and formal selection of the new name will take place in 2013. Construction on the Forth Replacement Crossing began in 2011 and is on schedule to open on schedule and on budget in 2016.
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Speaking on a visit to the existing Forth Road Bridge today, Mr Brown said: "This is the biggest single infrastructure project in Scotland for a generation and will deliver an iconic world class 21st century addition to the 20th century Forth Road Bridge and the original 19th century Forth Bridge.
"It is absolutely right that the people of Scotland have a say on the identity of this historic project and for that reason I am very happy to announce that a public vote on the naming will take place next year.
"I will shortly be appointing a panel of independent advisors to undertake a consultation on potential names. They will consider all possible suggestions before producing a shortlist of the most appropriate that can be put to a public vote.
"This is an exciting project that we want the people of Scotland to take pride in and I am delighted that the people of Scotland will have the opportunity to have the final say."
At the start of Scottish tourism week, Mr Brown also highlighted continuing efforts to have the historic 19th Century Forth Bridge recognised as a World Heritage Site: "On behalf of the Forth Bridges Forum, Historic Scotland are preparing to submit a Technical Evaluation document in support of the Forth Bridge's application for World Heritage Status.
"This is just the first round of the process. Transport Scotland, Network Rail and the surrounding local authorities are supportive of the bid and look forward to working with Historic Scotland on this important project."
(GK)
