DBS said in a statement to the Singapore Exchange that the deal "will accelerate DBS's ambition of becoming a leading wealth manager in Asia".
The acquisition comes at a time of growing competition to manage the wealth of Asia's growing ranks of millionaires and billionaires.
Under the agreement, DBS will buy Societe General's Asian private banking operations in Singapore and Hong Kong and parts of its trust business.
"This transaction is in line with one of DBS's strategic priorities to be a leading wealth manager in Asia and will significantly increase the scale of its wealth management business," Singapore's leading bank said.
Jean-Francois Mazaud, head of Societe Generale Private Banking, described DBS as "the most suitable choice".
"The commercial partnership we intend to implement together will also represent a great opportunity for our private banking customers to fully benefit from the very best of the two banks in Europe and in Asia," he said.
DBS's clients will have access to Societe Generale Private Banking's offerings in Europe, DBS said.
It said the deal would increase its high-net-worth assets under management by more than 20 per cent.
"From a strategic perspective, this acquisition will propel DBS forward in its strategy to grow its regional financial services footprint and become a leading bank in the Asian wealth management industry, which is a very fast-growing segment of the global financial services industry," said Rajiv Biswas, Asia Pacific chief economist at IHS Global Insight.
"The concentration of acquired assets in Singapore and Hong Kong is also positive in terms of the geographic distribution of assets under management, since Singapore and Hong Kong are the two leading international financial centres in Asia," he told AFP.
Kenny Kan, market analyst at CMC Markets in Singapore, said the deal marked a "strategic positioning" by DBS "in view of the growing need for wealth management in Asia with its ever-increasing millionaires".
DBS chief executive Piyush Gupta said in an internal memo to staff it was time for the Singapore bank to accelerate its private banking business through an acquisition.
"As you know, Asia is growing in affluence, and minting more millionaires every day than anywhere else in the world," he said in the memo, a copy of which was seen by AFP.