Milano was picked 16th overall in the 2014 NHL Draft and is coming off a solid season with the Blue Jackets’ AHL affiliate.
He had 14 goals and 31 points in 54 games with the Monsters, before adding another eight points in 17 playoff games en route to a Calder Cup championship.
The 20-year-old appeared in three NHL games last season, notching one assist.
In a corresponding move, the Blue Jackets have sent Oliver Bjorkstrand to Cleveland.
Bjorkstrand, a third-round pick in 2013, had no points in three games with Columbus this season and has seen his ice time dwindle.
He opened the season playing over 14 minutes, but has since seen his TOI reduced to 9:58 and 8:01 in his last two games.
The 21-year-old was also a big part of last year’s Calder Cup-winning Monsters team, having totalled 10 goals and six assists in the AHL post-season.