AT&T said Sunday that it had agreed to acquire America’s biggest satellite television provider, DirecTV, in a deal worth almost $50 billion. The boards of the two companies met on Sunday to approve the plan. “This is a unique opportunity that will redefine the video entertainment industry and create a company able to offer new bundles and deliver content to consumers across multiple screens — mobile devices, TVs, laptops, cars and even airplanes,” Randall Stephenson, the chief executive of AT&T, said in a statement. He described DirecTV as the “best option” for AT&T “because they have the premier brand in pay TV, the best content relationships, and a fast-growing Latin American business.” AT&T’s existing television service, called U-verse, only has about 5 million subscribers. DirecTV has more than 20 million.