GM Europe has not made a profit since 1999 and the deal has raised fears about job losses at Vauxhall.
The UK factories at Ellesmere Port and Luton employ about 4,500 people.
With GM's Opel and Vauxhall operations, PSA Group would become the second largest carmaker in Europe, behind Volkswagen.
In a statement, Carlos Tavares, chairman of PSA's managing board, said: "We are confident that the Opel/Vauxhall turnaround will significantly accelerate with our support, while respecting the commitments made by GM to the Opel/Vauxhall employees."
PSA said it would return Opel and its Vauxhall brand to profit, and expected to make savings of £1.47bn per year by 2026, with most of the cuts made by 2020.