In exchange, the Oilers will be sending defenceman William Lagesson, a conditional second-round draft pick and a seventh-round pick in 2024.
The Canadiens retain 50 per cent of Kulak's salary for the remainder of the season.
The Oilers' second-round pick comes with the following condition: if the Oilers reach the Stanley Cup Final, the pick will become a second-round selection in 2023.
Kulak, 28, is an eight-year NHL veteran who has spent the past four seasons with the Canadiens. In 56 games this season, Kulak has three goals and 13 points — the second-highest offensive output of his career.
Kulak carries a $1.85 million cap hit and will be an unrestricted free agent this summer.
It's no secret the Oilers have been looking for help on the blue line, the pressure mounting for general manager Ken Holland to shore up some help in their own zone in the hopes of also easing the burden on the crease. Considering how cap-strapped the club is this season, Holland's moves have been limited. Kulak brings depth to the Oilers' lineup as a dependable stay-at-home rearguard who plays a smart game.
The move is also a homecoming of sorts for Kulak, who hails from Stony Plain, Alta. -- just 40 minutes west of Edmonton.