The transaction will make Geely the biggest single shareholder in Volvo and the second biggest holder of voting rights.
The move represents another step by Geely - China's most-acquisitive auto maker - to become a global player.
According to press reports, Geely has "no plans" the Volvo vehicle and truck brands.
Chinese firm Geely, the maker of London's iconic black cabs and the owner of Volvo cars, has snapped up a stake in the Volvo truck business.
Volvo shares were down 1.5 percent to 157.6 Swedish crowns at 1050 GMT on December 27, valuing Geely's stake at roughly 26.4 billion crowns ($3.2 billion).
How the deal impacts Volvo's relationship with Chinese truck maker Dongfeng, in which Volvo has owned a 45% stake since 2015, is unclear.
The investment in AB Volvo is the latest step by the Chinese automotive group, founded and controlled by billionaire Li Shufu, to expand its footprint around the world. Geely and Cevian declined to disclose the exact value of the transaction.
"We will treat the new owners in the same way that we treat our other shareholders", a spokesman for AB Volvo said.
Volvo has also begun to reap the benefits from years of restructuring measures, including major cost-cutting programs, selling off non-core businesses, and management changes.
Under the terms of the agreement, Cevian will sell all of its 88.47 million A-shares and 78.77 million B-shares in Volvo to Nomura International and Barclays Bank, Geely and Cevian said in a joint statement.
In June, Geely Holding bought 49.9 per cent of Malaysian carmaker Proton and 51 per cent of iconic British sports vehicle marque Lotus Cars.
Industrivarden declined to comment when contacted by Reuters.