Per ESPN's Mike Reiss, the Patriots will receive a 2020 sixth-round draft pick in the deal, while Denver will receive Dawson and a 2020 seventh-rounder.
New England selected Dawson with the No. 56 overall pick in the second round of the 2018 NFL draft out of Florida.
While Dawson was expected to be a contributor at slot corner as a rookie, he did not appear in a regular-season game after being placed on injured reserve with a hamstring injury.
After failing to do much in New England's first three preseason games, Dawson registered three tackles and an interception in Thursday's 31-29 loss to the New York Giants.
Denver boasts a strong starting cornerback tandem in Chris Harris and Bryce Callahan, but there are major question marks beyond them. Having lost the likes of Aqib Talib and Bradley Roby in recent years, the Broncos are now relying on several inexperienced corners.
Prior to acquiring Dawson, 2018 third-round pick Isaac Yiadom was the top candidate to serve as the No. 3 cornerback. Yiadom appeared in 13 games as a rookie and finished with 20 tackles, three passes defended and one interception.
Yiadom may still have a leg up on Dawson due to his familiarity within Denver, but Dawson may have an opportunity to carve out an important role quickly given Denver's lack of other quality options.
The fact that New England got so little in return for a recent second-round pick suggests it was planning to release Dawson prior to the final roster cut-down on Saturday.
The Pats boast a great deal of depth at corner with starters Stephon Gilmore and Jason McCourty followed by J.C. Jackson, Jonathan Jones, Keion Crossen, Obi Melifonwu, rookie second-round pick Joejuan Williams and rookie seventh-round pick Ken Webster.
Even with Dawson no longer in the picture, head coach Bill Belichick will have several difficult decisions to make with regard to the cornerback position.