The 44-year-old was sacked by Ipswich in October after just five months in charge and has been out of work since.
Scunthorpe were relegated to League Two on the final day of the League One season.
Andy Dawson had been in temporary charge of the club following Stuart McCall’s departure in March and he will revert to his position on the coaching staff.
Hurst had impressed at Shrewsbury, taking over in October 2016 when the club were bottom of League One and leading them to an 18th-place finish.
The Shrews finished third the following season, losing to Rotherham in the Play-Off Final at Wembley.