The deal is worth $5 million, a source told ESPN's Adam Schefter.
Cobb visited with the Cowboys at The Star on Monday, taking a physical and meeting with coaches and staff. The club also met with safety Clayton Geathers on Monday, with safety Eric Berry, defensive lineman Malik McDowell and defensive end Robert Quinn visiting on Tuesday.
Quinn and Berry concluded their visits without any deals pending. Quinn is scheduled to visit with the New Orleans Saints, while Berry is looking at other options as well.
The Cowboys and Miami Dolphins have had discussions regarding a trade for Quinn, according to multiple sources.
Cobb fills a need after the Cowboys lost slot receiver Cole Beasley in free agency to the Buffalo Bills last week on a four-year, $29 million deal that included $14.4 million in guaranteed money. Cobb joins Allen Hurns and Tavon Austin as slot players on Dallas' roster. Hurns is coming back from a gruesome ankle injury suffered in a wild-card win in January against the Seattle Seahawks; Austin agreed to a one-year deal last week.
Cobb, who spent his first eight NFL seasons with the Green Bay Packers, has played parts in ending two of the Cowboys' last three playoff seasons (2014, '16). Now the Cowboys hope he can help extend their postseason success by helping Dak Prescott.
The new Cowboy took to Twitter on Tuesday to share his thoughts on the deal.
Cobb, who turns 29 in August, was limited to just nine games in 2018 because of hamstring injuries and a late-season concussion. He caught just 38 passes for 383 yards and two touchdowns -- all lows since his 91-catch, 1,287-yard, 12-touchdown season of 2014.
It was after that season when he signed a four-year, $40 million contract.
Despite Cobb's limited production, quarterback Aaron Rodgers stated the receiver's importance to the Packers offense late in the season when he said: "When Randall's healthy, I think our offense has been different because we have a true slot guy who can make plays in the slot consistently."
Cobb, a second-round pick (64th overall) in 2011, is one of just five players in Packers history with at least 60 catches in four straight seasons (2014 to 2017). He ranks sixth in franchise history with 470 catches and 11th in both receiving yards (5,524) and touchdown catches (41).
ESPN's Rob Demovsky contributed to this report.