Budish, who had one year of eligibility remaining at the University of Minnesota, signed a two-year, two-way deal worth $1.15 million.
He is the second player from the Gophers to sign a two-year deal with an NHL team in the past two days. Undrafted defenseman Nate Schmidt inked a two-year deal with the Washington Capitals on Tuesday. Forward Nick Bjugstad, a first-round pick by the Florida Panthers in 2010, also signed a three-year entry-level deal Wednesday.
Budish finished his junior season with 36 points, including 14 goals, 22 assists and a plus-17 rating in 40 games. The 6-foot-3, 214-pound player, who was selected No. 41 in the 2009 NHL Draft, had 35 goals and 94 points in 129 career games with the Gophers.