The Italian carmaker first began building stock in Chrysler as part of a government and union-led bailout for the struggling company, culminating in a majority share in 2011.
The remaining share, a 41.46 percent stake held by United Auto Workers’ retirees’ healthcare trust VEBA, will be purchased at a cost of US$3.65 billion.
The purchase will be made up of a US$1.75 billion contribution from Fiat and US$1.9 billion from Chrysler - currently the more profitable arm of the alliance.
Once the deal closes, Chrysler will pay an additional US$700 million to the trust through four annual payments, contributing to the medical benefits of Chrysler retiree funds managed by VEBA.
The deal, which will help to realise the global growth plans of Fiat and Chrysler boss Sergio Marchionne, is expected to close by January 20.
"The unified ownership structure will now allow us to fully execute our vision of creating a global automaker that is truly unique in terms of mix of experience, perspective and know-how, a solid and open organization that will ensure all employees a challenging and rewarding environment," Mr Marchionne said.
"In the life of every major organization and its people, there are defining moments that go down in the history books. For Fiat and Chrysler, the agreement just reached with the VEBA is clearly one of those moments."
Fiat Chairman John Elkann echoed Marchionne's comments, adding that he has been looking forward to this day since the Fiat-Chrysler alliance was first announced.
"The work, commitment and achievement I have witnessed from Chrysler over the past four and a half years is nothing short of exceptional, and I take this opportunity to officially welcome each and every one of the people in the Chrysler organization to the integrated Fiat-Chrysler world."
In Australia, the impact of Fiat's revitalised global management system has fed sales growth of the brand, with 2013 sales far outstripping the previous year.
While full-year VFACTS figures are still to come, November numbers show that Fiat and Alfa Romeo have moved some 5211 cars for the year, compared to 1267 in 2012.
The significant growth is thanks largely to a switch to factory control from previous distributor Ateco, along with an injection of new models and - most importantly - a major price shuffle across the range.
Likewise, Chrysler brand sales in Australia grew to 23,896 (YTD end-November) in 2013 from 19,359 in 2012, thanks again to a refocused Fiat-led business plan and - for the Chrysler and Jeep marques - important new models.
Only the Dodge brand failed to find growth in 2013, with sales falling from 1905 in 2012 to 1477 in 2013.
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