The deal is worth $5 million, sources told ESPN's Adam Schefter.
Cobb was a dynamic slot receiver and returner and a Pro Bowler during his prime years.
The now-former Packers slot receiver tweeted a picture of the popular Toy Story character, Woody shortly after the report was announced seemingly confirming the deal. The official schedule should be out in the next month. The Patriots reportedly are among the teams interested in the 33-year-old Nelson, who caught 63 passes for 739 yards and three touchdowns last season.
Cobb spent the first eight years of his National Football League career with the Green Bay Packers, though he was limited to nine games last season because of a hamstring injury and a concussion.
The Cowboys tried to address their receiver situation in the offseason and might have been better off not winning a bidding war for Sammy Watkins. As another receiver who operates out of the slot, Cobb could be a natural replacement for some of Beasley's routes.
Cobb appeared to acknowledge the move on Twitter. But Cobb would be an exciting addition to a Cowboys offense which has lacked "creativity" over the last few seasons, and is looking to reinvent themselves to a certain extent.
Heading into last season, the biggest question for the Dallas Cowboys was their receiving corps.