Wednesday's deal will allow Chrysler to avoid an IPO.
In a statement, Marchionne called the buyout a defining moment for the two companies.
"The unified ownership structure will now allow us to fully execute our vision of creating a global automaker," he said.
The Chrysler buyout talks have been closely watched by debt and equity investors as Fiat's long-term plan to cut losses in Europe depends on its ability to deepen ties with Chrysler.
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Chrysler is now a profit center for Fiat, but the two companies currently are forced to manage their finances separately. A full merger will make it easier - but not automatic - to combine the cash pools of the two companies, giving Fiat more funds to expand its product lineup.
The UAW trust was created in 2007 as a way for General Motors Co, Ford Motor Co and Chrysler to offload their obligations to pay retiree healthcare benefits.
Medical benefits for GM, Ford and Chrysler retirees are handled in separate accounts and each account was initially to be funded with cash. But during the 2009 financial crisis, the VEBA agreed to accept stakes in GM and Chrysler in lieu of cash.