Michigan's season ended with a 3-2 overtime loss to the University of Denver on Thursday in the NCAA Frozen Four semifinal round in Boston.
In two seasons with Michigan, Johnson had 64 points (17 goals, 47 assists) in 58 games.
Johnson scored one goal in two games for Canada at the 2022 IIHF World Junior Championship before the tournament was postponed due to concerns surrounding the coronavirus. He also had five points (one goal, four assists) in five games at the 2022 Beijing Olympics.
The Blue Jackets also signed Johnson's teammate, undrafted defenseman Nick Blankenburg on Friday to a one-year, entry-level contract for the remainder of the season. The Michigan captain had 29 points (14 goals, 15 assists) in 38 games as a senior this season and 68 points (25 goals, 43 assists) in 133 games with the Wolverines.
"You can just see during games his deception with the puck is unbelievable and just the way that he makes guys think he's going one way and then he'll just be going the complete other way," Blankenburg said of Johnson.
"He's pretty strong on the puck, which for a guy who's 5-11, 165-170 pounds, he's pretty hard to knock him off the puck, which is pretty special, so I'm excited to watch him play at the next level and happy that I maybe get to do it with him."
NHL.com independent correspondent Craig Merz contributed to this report