The board of PSA, which makes Peugeot and Citroen cars, approved the deal on Friday, with an announcement planned for Monday, one of the people said.
Spokespeople for PSA and Opel declined to comment.
The two carmakers, which already share some production in an existing European alliance, confirmed last month they were negotiating an outright acquisition of Opel and its British Vauxhall brand by Paris-based PSA, sparking widespread concern over possible job cuts.
Earlier on Friday, Opel managers had adjourned a town hall meeting with workers until Monday morning, saying they could not yet discuss details of the proposed deal. Sources close to the GM-PSA talks had said on Thursday they were progressing well after the carmakers narrowed differences on about $10 billion in Opel pension liabilities and other issues. GM's European arm recorded a 16th consecutive year of losses in 2016.
The talks had also encountered difficulties over GM demands that a PSA-owned Opel be barred from competing against its own Chevrolet lineup in China and other overseas markets, they said. The "non-compete" issues were finally resolved as GM agreed to inject "substantially" more into the pensions than the $1 billion to $2 billion it had initially offered, another person said on Friday.
The sources declined to give any further details. PSA boss Carlos Tavares said last week a full acquisition of Opel offered an "opportunity to create a European car champion" and quickly exceed 5 million annual vehicle sales. The French carmaker also expects savings of up to 2 billion euros ($2.1 billion) from the tie-up, sources have said. Tavares told his board that PSA would redevelop the core Opel lineup with its own technologies to achieve rapid savings, according to people with knowledge of the matter.