The offer values Poland's No.11 lender by assets at almost 4.52 billion zlotys ($1.43 billion) 16 percent above Monday's closing price, and more than the 4.2 billion purchase tag BNP agreed with Rabobank last year.
The European Commission has already approved the merger, but BNP is awaiting a green light from the Polish watchdog KNF.
Citigroup's Polish unit, which is coordinating BNP's offer, said BGZ owners will be able to sell their shares between Sept. 12 and Oct. 17. BNP wants to buy 100 percent in BGZ and plans to merge it with its small-tier Polish unit.