Italian automaker Fiat plans to take full control of Chrysler Group by buying out the shares held by a United Auto Workers union-controlled trust fund.

The union and Fiat reached a deal on New Year’s Day for the automaker to acquire the 41.5% of Chrysler’s shares that were held by the UAW Retiree Medical Benefits Trust.

Fiat already acquired the rest of Chrysler’s shares through a deal launched during the bankruptcy restructuring of the Auburn Hills, Mich., automaker in 2009.

This deal is worth $4.35 billion to the union. Fiat will pay about $1.75 billion upfront. The trust fund will receive another $1.9 billion in payments through special Chrysler dividends. The deal is expected to close by Jan. 20. Additionally, the merged automaker will make another $700 million in payments to the trust over four years.

The UAW and Fiat have fought for several years over how to reach a fair price for the shares.

While Fiat and Chrysler have already been operating as one company in many ways, this deal enables the two to integrate more fully and gives Fiat access to Chrysler’s cash, said Stephanie Brinley, an analyst at IHS Automotive.

That’s an important move. Fiat’s financial results have been dragged down by the continuing financial malaise in Europe, its primary market.

Meanwhile, Chrysler posted a 22% gain in profit, to $464 million, in its most recent quarter compared with the same period a year earlier. The third quarter was the automaker's ninth consecutive quarter of positive net income. Revenue grew 13.5% to $17.6 billion, helped by sales of the company's Jeep Grand Cherokee and Ram pickup trucks.

The U.S. auto market is strong and is on track to increase its sales by 50% over its lows in the past recession.

“Whether the company has a dominant Italian flavor, dominant American flavor, or something altogether new remains to be seen,” Brinley said.

In an email to employees, Sergio Marchionne, who already serves as chief executive of Fiat and Chrysler, called the merger agreement “an historic moment” for the car companies.

He said it was the logical conclusion to the previous efforts by the two automakers  “to integrate our respective cultures, transform our differences into strengths and break down geographic and cultural barriers. “

“The result has been the creation of a global automaker that is among the leaders in the sector,” Marchionne said.

Brinley called the merger “a victory for Marchionne, who had been looking for a partner to deliver the scale Fiat needs since 2004, and has succeeded.”

This will be the second time Chrysler has been owned by a foreign automaker.

Daimler-Benz, the owner of Mercedes-Benz, acquired what was then called Chrysler Corp. in 1998. The combination was supposed to enable the German automaker to leverage its famous engineering and the strong position Chrysler occupied in North America.

But synergies between the two companies — with vastly different corporate cultures — proved elusive. Daimler sold Chrysler to Cerberus Capital Management in 2007. Then the recession hit, sending Chrysler into bankruptcy in 2009.

The federal government led the effort to remake Chrysler as part of a $12.5-billion bailout that, along with the $51-billion rescue of General Motors Co., was designed to save the U.S. auto industry during the depths of the recession.

Fiat purchased the government's remaining stake in Chrysler in 2011, ending the bailout with a taxpayer loss of $1.3 billion.

The union trust provides medical coverage for about 115,000 retired Chrysler workers and their families.

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