Shareholders of Reebok International Ltd. (RBK) voted Wednesday to approve the $3.8 billion sale of the sports sneaker and apparel maker to Adidas-Salomon AG, a deal that seeks to challenge Nike Inc.'s (NKE) market leadership.

Reebok shareholders' approval was the final hurdle for a deal that won European Union regulatory approval on Tuesday. U.S. regulators did not raise any antitrust objections after Canton-based Reebok and Germany's Adidas-Salomon announced the friendly takeover on Aug. 3.

Reebok said more than 98 percent of the votes were cast in favor of the transaction. Adidas' price would give Reebok shareholders a 34 percent premium over Reebok's share price before the deal was announced.

The two companies had said they expected to close the acquisition in the first half of this year, and Wednesday's vote by Reebok shareholders puts the companies on track to close the deal early in that time window. Reebok said Wednesday the companies now expect to close the deal by Jan. 31.

Reebok had been hoping for a speedy conclusion in part because the company acknowledged three months ago that uncertainty surrounding the deal and the companies' integration plans had hurt sales and orders to retailers.

Adidas-Salomon expects the deal will double its U.S. business and narrow the gap held by Beaverton, Ore.-based Nike, the world market leader. The deal will create a company with combined annual sales of nearly $12 billion, bringing together Adidas' popularity in Europe among soccer fans with Reebok's strengths among basketball and football fans in North America and among buyers who consider sneakers high fashion.