"The transaction that we are announcing today represents a historic step for Fiat and Chrysler," Fiat chairman John Elkann said in a statement.
Fiat already owns a 30-per cent stake in the US auto company.
The deal will take place over the course of the second quarter and US and Canadian government debt in Chrysler will be "fully repaid", Fiat said.
Fiat took over management of troubled Chrysler after its 2009 bankruptcy as part of an agreement for a gradual merger between the two firms.
"This is a fundamental step toward completion of the momentous integration of Fiat and Chrysler," said Fiat boss Sergio Marchionne, who is also the chief executive of Chrysler.
The statement added: "Fiat, together with Chrysler, will create a stronger automobile group, with a full range of products, present in every market around the world and able to compete with the best."
Marchionne said in February that Fiat and Chrylser would fully merge within two or three years.
Fiat shares shot up 2.43 per cent to 6.735 euros in early trading in Milan.