Coan beat out sophomore Drew Pyne and freshman Tyler Buchner for the starting job.
"All three quarterbacks distinguished themselves in the spring and preseason camp," Kelly wrote in a tweet. "Clearly, each has the skills necessary to lead, but Jack proved to be more consistent and therefore, going into our opener, gives us the best chance for success."
Coan started 18 games for the Badgers through three seasons, including a Big Ten championship game and a Rose Bowl. He completed 236 of 339 passes for 2,727 yards, 18 touchdowns, and five interceptions in his only full season as a starter before a broken foot in camp last year sidelined him for the season.
Graham Mertz grew into Wisconsin's top quarterback, which led Coan to transfer to Notre Dame. Coan originally committed to the Irish to play lacrosse before deciding he wanted to play college football. If each quarterback stays healthy and holds down the No. 1 spot for their respective teams, Coan and Mertz will duel Sept. 25 when the Irish play Wisconsin at Soldier Field in Chicago.
Coan takes over for Ian Book, who led Notre Dame to the College Football Playoff in two of his three seasons as the team's starting quarterback. The New Orleans Saints selected Book in the fourth round of this year's NFL Draft.
Pyne returns to a role as No. 2, which he took during the second half of the 2020 season when Brendon Clark was sidelined with a knee injury. The injury has kept Clark out of the Irish's first week of camp. Buchner, a former top 100 prospect, will be third on Notre Dame's QB depth chart.