Joshua has also agreed to a two-year entry-level deal with the Blues.
"Dakota has had an outstanding college career and we are excited to be adding him to our team," Armstrong said.
The 23-year-old recently completed four years at Ohio State, where he accrued 41 goals and 100 points in 128 games. Joshua was named to the 2018 NCAA Midwest Regional All-Tournament Team, Honorable Mention All-B1G in 2017 and was a two-time Ohio State Scholar-Athlete and Academic All-Big Ten.
A native of Dearborn, Mich., Joshua was selected in the fifth round (128th overall) by Toronto at the 2014 NHL Draft.