The changes will also see the new company renamed Fiat Chrysler Automobiles, after its merger with US automobile group Chrysler, and be domiciled in Britain.
"The future of our company begins with the meeting today," said Fiat president John Elkann, before the vote in the carmaker's historic headquarters in Turin.
The move turns a page in Fabbrica Italiana Automobili Torino's 115-year history and will transform the Italian carmaker into the world's seventh-largest automobile giant.
"There were so many beautiful memories. I wish you good luck, with tears in my eyes," one woman told the meeting.
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Chief executive Sergio Marchionne said the merger "signals after 115 years the end of a long, historic cycle," but also opens "a new future... With strong and concrete prospects".
But not all shareholders were behind the deal, with some labelling it as "not credible".
The new group is slated to list on the New York Stock Exchange in the first half of October.
Fiat has set a maximum payout of 500 million euros. But Marchionne brushed off concerns today that this level could be breached given the amount of opposition to the deal, adding he was "not worried".
The deal comes at a difficult time for carmakers on both sides of the Atlantic, which have suffered as demand crashed during the global financial crisis.
France's industry body said today that the car sales fell 4.3 per cent in July as economic jitters weighed on demand, while last month saw the second-lowest sales for June on record, according to Europe's carmaking lobby group.