"We are happy to have come to an agreement with Davis on a two-year contract. He brings experience and most importantly depth to our group of defensemen," Canadiens general manager Marc Bergevin said.
In 29 games with the Los Angeles Kings and Canadiens in 2012-13, 28-year-old Drewiske totaled two goals and seven points, along with 14 penalty minutes and a plus-3 rating.
The 6-foot-2, 220-pound blueliner has five goals and 25 points in 135 NHL regular-season games.
A native of Hudson, Wis., Drewiske was acquired from the Kings on April 2, 2013 in return for a fifth-round pick at the 2013 NHL Draft.