The Pittsburgh Penguins didn't tender a qualifying offer to Poehling on Friday. The 24-year-old tallied seven goals and 14 points in 53 games last season.
The Montreal Canadiens drafted Poehling 25th overall in 2017. He burst onto the scene in 2019, scoring a hat trick and a shootout goal against the Toronto Maple Leafs in his NHL debut.
Pittsburgh acquired Poehling last summer as part of the package in the Jeff Petry trade.
Poehling has 20 goals and 36 points in 136 career NHL games.
The Montreal Canadiens are trading defenseman Joel Edmundson to the Washington Capitals for third-round and seventh-round selections in the 2024 draft, the teams announced.
The Habs are retaining 50% of Edmundson's $3.5-million cap hit, per Sportsnet's Elliotte Friedman. He has one year remaining on his deal.
Edmundson recorded 13 points, 112 hits, and 149 blocks in 61 games last season while averaging 19:34 of ice time per contest.
Brannstrom, 23, was slated to become a restricted free agent after being tendered a $945,000 qualifying offer from the Sens on Friday.
The former first-round pick scored two goals and added 16 assists last year while averaging 16 minutes of ice time over 74 games. He primarily played on the third pairing.
Brannstrom has four goals and 45 assists in 190 career contests.