"Chrysler Group is now a wholly-owned subsidiary of Fiat," the Italian company said in a statement.
The deal involved buying the remaining 41.46 percent stake in Chrysler not held by Fiat from Veba, a fund controlled by the US autoworkers' union UAW.
Fiat and Chrysler together make the world's seventh biggest auto group and the name of the merged company and the choice of location for its headquarters are due to be announced at a board meeting on January 29th.
Sergio Marchionne, who is the chief executive of both Fiat and Chrysler, said this month he was considering a possible listing on the Hong Kong or New York stock exchanges and would aim for a premium car market.
Asked about financing for Fiat-Chrysler, Marchionne said that a convertible bond issue was "appropriate" but a final decision would be up to the board.
"We are here, ready to go, but we need money to go," he said.
A convertible bond is a type of bond that can be converted into shares in the issuing company or cash of equal value. They are often used by companies with a low credit rating but high growth potential.
Fiat's results have been hit by the plunge in sales on its domestic market and have been propped up by Chrysler's return following a bankruptcy procedure.
The merger procedure began in 2009.
Marchionne was welcomed as a hero at the Detroit Auto Show last week after sealing the deal following months of tough negotiations.