The announcement ends weeks of speculation about the deal and its impact on thousands of jobs at Vauxhall plants in Ellesmere Port and Luton.
The announcement said the transaction will allow “substantial economies of scale and synergies” in purchasing, manufacturing and research and development.
PSA, together with BNP Paribas, will also acquire all of GM Financial’s European operations through a newly formed 50%-50% joint venture.
Unite called for assurances over the long-term future of the UK factories.
PSA will become the second-largest automotive company in Europe, with a 17% market share.
“We are proud to join forces with Opel/Vauxhall and are deeply committed to continuing to develop this great company and accelerating its turnaround,” said Carlos Tavares, chairman of the managing board of PSA.
“We respect all that Opel/Vauxhall’s talented people have achieved as well as the company’s fine brands and strong heritage. We intend to manage PSA and Opel/Vauxhall capitalising on their respective brand identities.
“Having already created together winning products for the European market, we know that Opel/Vauxhall is the right partner. We see this as a natural extension of our relationship and are eager to take it to the next level.
“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.”
Mary Barra, chairman and chief executive of GM, said the deal created a new opportunity to enhance the long-term performance of the respective companies, adding: “For GM, this represents another major step in the ongoing work that is driving our improved performance and accelerating our momentum.
“We are reshaping our company and delivering consistent, record results for our owners through disciplined capital allocation to our higher-return investments in our core automotive business and in new technologies that are enabling us to lead the future of personal mobility.
“We believe this new chapter puts Opel and Vauxhall in an even stronger position for the long term and we look forward to our participation in the future success and strong value-creation potential of PSA through our economic interest and continued collaboration on current and exciting new projects.”
Len McCluskey, general secretary of Unite, said thousands of Vauxhall workers at Ellesmere Port and Luton had endured a “nerve-racking” few weeks.
“While initial discussions with the PSA Group have been relatively positive, our priority now is to ensure a long-term future for our plants and the tens of thousands of workers depending on them,” he said.
Luton South’s Labour MP Gavin Shuker said: “Glad to see the uncertainty over the PSA/GM deal is now over.
“Our UK plants are among the most efficient of any in the new company. They deserve a bright future.
“Now Government needs to play its part, delivering a Brexit deal that keeps Vauxhall building in the UK.”