Braunecker, 25, has played in 36 games for the Bears over the past three seasons. A backup who has largely been used as a blocker and member of the special teams unit, he has seven receptions for 83 yards, and 11 tackles.
An unsigned free agent from Harvard, Braunecker was due to become a restricted free agent at the start of free agency on Wednesday, but the bears locked him up for the next two seasons instead.
Teams were allowed to begin negotiating with free agents on Monday, but cannot officially sign them until Wednesday.
Braunecker might end up with a greater role on the Bears in 2019, as the team cut ties with Dion Sims earlier in the offseason.
Fellow tight end Daniel Brown is set to be an unrestricted free agent.
The Bears have 17 players from the 2018 roster who are set to become free agents on Wednesday, including safety Adrian Amos, nickel cornerback Bryce Callahan, punter Patrick O’Donnell, wide receiver Joshua Bellamy, outside linebacker Aaron Lynch, guard Eric Kush, guard Bryan Witzmann, and long snapper Patrick Scales.