The deal would also provide funds to the ailing Australian company's development and research on new products to maintain its leading position in the global market.
Geely will retain the DSI brand and its independence to ensure services to global clients, the statement said.
However, the company did not disclose any financial figures and details about the transaction.
DSI, with more than 80 years of history, was OEM (original equipment manufacture) supplier for leading automakers like Ford, Chrysler and Ssangyong Motor. It has an annual capacity of 180,000 automatic transmission systems.