Harris was selected in the first round, 29th overall, by Toronto.
The Blue Jays announced that they have signed 30 of their 40 selections, including eight of their top 10 picks. Eight non-drafted free agents were also signed following the draft.
Harris, from Florissant, Mo., attended Missouri State, helping the Bears to a 2015 Missouri Valley Conference Championship and a Super Regional appearance.
The 21-year-old Harris has a 19-9 record over three NCAA seasons with a 3.09 earned-run average and 243 strikeouts in 43 games.