The EU said it saw no competition problems with the deal since the combined firm would continue to face strong rivals and existing customers still would have a range of suppliers to choose from.
In August, BPB rejected Saint-Gobain's offer, saying it substantially undervalued the company. It earlier turned down two friendly approaches.
BPB, the world's largest producer of plasterboard and gypsum plasters, claims the global plasterboard market has grown more than 60 percent over the last 10 years, with BPB's organic growth over this period at 6.5 percent per year outperforming the market growth of around 5 percent per year.
Saint-Gobain, one of the world's largest suppliers of glass, insulation and other building materials, said it would ask shareholders to decide on the bid.
It argued that Saint-Gobain's strong presence in the North American plasterboard market complemented Saint-Gobain's wall-siding, roofing and insulation products portfolio in the region.
Analysts have been surprised by Saint-Gobain's sudden bid for a plasterboard maker, a sector from which it is now absent, and say it marks a departure from the company's previous focus on developing its building materials distribution and high performance materials divisions.