Milan-based automaker Fiat SpA (FIATY.PK) announced on Tuesday that Chrysler Group is now “wholly owned” by it, closing the book on a deal that has been in the making for some time now. Fiat gained a controlling stake in Chrysler and its brands in 2009, as part of the American auto industry’s bailout arrangement. What wasn’t held by Fiat at the time was given to a retiree health care trust controlled by the United Auto Workers, and after months of negotiations, the UAW trust agreed to relinquish its position for $4.35 billion.

“We reached a successful conclusion that will benefit the trust’s retirees,” Robert Naftaly, chair of the committee that operates the trust, said in a statement. “This was always our goal. As a result, the Trust is stronger.”

The job isn’t over for Fiat, though. The firm has a meeting set for January 29 to determine how best to complete the merger of Fiat and Chrysler, where the combined company will be registered, what it will be called, and where its stock will be traded, the Detroit News reports.

According to Fiat CEO Sergio Marchionne, the combined company will incorporate both the Fiat and Chrysler names. Fiat is currently traded on the Milan exchange, though Marchionne said, per the Detroit News, that the combined entity would likely list in New York to “ensure easy access to the capital markets.”

The UAW trust — which manages several hundred thousand retires from Ford, General Motors, and Chrysler — still has a guarantee from Chrysler for about $4.8 billion as a part of the deal. Marchionne, though acknowledging that it is a substantial amount of money, doesn’t appear to be concerned, since it will be wrapped up in the greater dealings when the merger is sorted out on paper. “It’s a costly note,” the Detroit News reports him as saying last week. “We’re looking at this as part of the whole finance structure.”

The ink isn’t dry yet, and Fiat has already turned its attentions toward improving Chrysler’s struggling line of cars. The new 200 sedan recently made its debut at the Detroit auto show to a generally warm reception. The Ram 1500 pickup was one of America’s best-selling vehicles last year, and Jeep has done some pretty significant work to its lineup, as well.