He had three points in nine games for the Habs after being acquired in a trade with the Los Angeles Kings on April 2 in exchange for a fifth-round draft pick.
"We are happy to have come to an agreement with Davis on a two-year contract," Canadiens general manager Marc Bergevin said in a release. "He brings experience and most importantly depth to our group of defencemen."
The six-foot-two, 220-pound blue-liner had seven points (2-5) in 29 games with the Kings and Canadiens this past season while averaging just over 15 minutes of ice time per game.
Drewiske, a 28-year-old native of Hudson, Wis., has 25 points (5-20) in 135 career NHL regular-season games.