The deal ties in with plans by Millennium's Portuguese owner BCP to find new areas of growth and indicates the trend towards consolidation in the fragmented Polish banking sector.
SocGen, one of the lowest-scoring banks in the latest European stress tests, is shedding assets to focus on its core businesses. It announced a deal in August to sell its banks in Bulgaria and Albania to Hungary's OTP Bank.
The Polish sale will lead to a 2 billion euro ($2.3 billion) reduction in SocGen's risk-weighted assets and boost its tier-one capital ratio by 8 basis points.
Analysts at brokerage Jefferies wrote that the EBA's stress test was of limited impact for SocGen and other French banks, since "the capital positions have improved materially since the last test."
Despite its low ranking, SocGen nevertheless passed the threshold set by the European Banking Authority (EBA) in the latest health check on the sector.
Analysts at Keefe, Bruyette & Woods (KBW) also said the deal was a good one for parent company BCP.
"At first glance we believe this transaction will be well received," wrote KBW, which kept an "outperform" rating on the shares of Portugal's BCP.
Euro Bank is the 17th largest Polish bank with assets of 14 billion zlotys, and is more than 20 times smaller than the country's biggest lender PKO BP. Last year, it made a net profit of 103 million zlotys.
Millennium, the seventh largest player in Poland, said its distribution network would more than double thanks to the takeover. It added at a presentation on Monday that it saw integration costs from the deal at 350 mln zloty over the 2019-2022 period, with 650 million zloty of synergies in 5 years from the acquisition.
Societe Generale said it would continue to provide Corporate and investment banking services in Poland and will remain present in the country in various other activities.
The deal is expected to close in the first half of 2019 and is still subject to the approval of Poland's financial market regulator KNF and antimonopoly authorities.
Bank Millennium also said it did not plan to issue new shares to finance the deal.
(Reporting by Sudip Kar-Gupta in Paris and Agnieszka Barteczko in Warsaw; Additional reporting by Lawrence White in London; Editing by Gopakumar Warrier/Keith Weir)
By Marcin Goclowski and Sudip Kar-Gupta