MILAN/DETROIT, Jan 1 (Reuters) - Italian carmaker Fiat SpA said on Wednesday it has signed an agreement to buy the stake in U.S. automaker Chrysler Group LLC it does not already own, ending months of tense negotiations and allowing Chief Executive Sergio Marchionne to pursue his goal of creating the world's seventh-largest auto group.

Fiat will acquire the 41.46 percent stake in Chrysler from a retiree healthcare trust affiliated with the United Auto Workers union, which will receive $3.65 billion in cash for its stake. Additionally, once the deal closes, Chrysler has committed to giving the trust an additional $700 million.

The deal is a victory for Marchionne, who wants to merge Fiat and Chrysler and create a more competitive automaker with a broader global reach. But he has been at odds with the UAW trust for more than a year over the value of Chrysler.

Chrysler will contribute $1.9 billion in cash, while Fiat will put up $1.75 billion to buy out the trust, which is known as the VEBA, both companies said in separate news releases.

In addition, Chrysler said it signed agreement with the UAW to pay a total of $700 million in four equal annual payments to the VEBA after the Chrysler stake sale closes. The VEBA manages and pays for medical benefits for Chrysler retirees.

The deal is expected to close on or before Jan 20. In view of the financial structure of the deal Fiat said it would not need to make any capital increase through a rights issue.

Marchionne has led both automakers since 2009. The Fiat-Chrysler alliance was one of the centerpieces of the Obama administration's 2009 restructuring of the U.S. auto industry.