The Bears signed Thompson to a reserve/future contract Monday.
Thompson finished the season on the Bears' practice squad but will need to put together an impressive offseason in order to stick with the team into the 2018 regular season.
Thompson will sign with the Bears' practice squad Tuesday, Brad Biggs of the Chicago Tribune reports.
An undrafted rookie tight end out of Temple, Thompson took part in training camp with the Giants, but was cut loose after requiring an appendectomy. Now apparently back to full strength, Thompson could earn a promotion to the Bears' active roster if he impresses in practices. The Bears lost starting tight end Zach Miller (knee) to a likely season-ending injury and career-threatening injury in their last game Oct. 29 against the Saints.
Thompson was waived by the Giants on Monday after undergoing an appendectomy, Michael Elsen of Giants.com reports.
Thompson figured to have slim odds for making the final roster before the procedure. He is expected to clear waivers, and subsequently revert to the team's injured reserve. The 23-year-old is likely to spend the entirety of 2017 there unless he and the team reach an injury settlement.