PSA said the acquisition, announced on 6 March, would position it as the second largest automotive company in Europe and would be the basis of the group's profitable growth worldwide.
"This proposed acquisition of GM's European financial operations is also subject to EU antitrust authority's review and the decision is expected in the second half of this year."
Patrice Lucas, manager of programs and group strategy said in a statement: "Today, we have taken a substantial step. The teams are now focused on the achievement of all other conditions necessary for the closing, planned for later this year."
Last month, Opel CEO Karl-Thomas Neumann stepped down as the speaker of the management board and CEO of Opel/Vauxhall.
Michael Lohscheller, Opel CFO since September 2012, was appointed his successor immediately.
Neumann remains a member of the management board until the closing of the sale.
There had been speculation a closing could be completed by the end of July.