A source told ESPN that deal is worth $2.5 million.
A source said the addition of Thompson does not close the door on the Cowboys' interest in wide receiver Allen Hurns, who visited the team Wednesday and had dinner. Hurns was released by the Jacksonville Jaguars earlier this week.
Thompson, 29, led the Buffalo Bills with 318 receiving yards over the final two months of the 2017 season. He started seven of Buffalo's final eight games.
The Bills signed Thompson in October to bolster a group of receivers that was the NFL's least productive through the first month of the season. He played the first five games of the season for the Chicago Bears before being released.
In 16 games this past season for Chicago and Buffalo, Thompson set career highs with 38 catches and 555 receiving yards, while tying his career high with two touchdowns.
An undrafted free agent in 2012, Thompson played only 21 games over his first four seasons for the Baltimore Ravens, Bills and Bears before emerging to start six games for Chicago in 2016.
ESPN's Mike Rodak contributed to this report.