NFL Network first reported the deal.
Burton, 26, has a special place in Eagles history because of his role in the "Philly Special." During that trick play in Super Bowl LII, Burton threw a touchdown pass to quarterback Nick Foles off a reverse handoff.
Due largely to the presence of veteran tight ends Zach Ertz and Brent Celek, Burton was only on the field for 27 percent of the offensive snaps last season, but he made the most of his opportunities, hauling in 23 passes for 248 yards and five touchdowns. He was a key special-teams contributor for the Eagles, finishing third with nine tackles last season; he also came up with a fumble recovery.
The Bears are adding playmakers for young quarterback Mitch Trubisky. Former Jaguars wide receiver Allen Robinson, who has 202 catches for 2,848 yards and 22 touchdowns in 43 games, also intends to sign with the team, ESPN has learned.
In his four seasons with the Eagles, Burton -- who also played quarterback at Florida -- has caught 63 passes for 629 yards and six touchdowns and also has scored on special teams.
The Bears will also add former Dolphins kicker Cody Parkey, a source told ESPN's Adam Schefter.
ESPN's Tim McManus contributed to this report.