The 23-year-old, who is a former youth international, has signed a three-year contract at the Britannia Stadium which will take affect from July 1st.
Haugaard is expected to link up with his new teammates at the Clayton Wood Training Ground for the start of pre-season training two days later, on July 3rd.
Announcing the news, Chief Executive Tony Scholes told stokecityfc.com; "We are delighted to have captured our second signing of the close season, by bringing Jakob to the Club.
"He is a goalkeeper that has been admired from afar by our first-team management for some time now so naturally we are pleased to have been able to conclude the deal.
"With Thomas Sorensen departing this summer, adding an additional goalkeeper to the squad had been highlighted as something of a priority for us."
The giant stopper has made 24 appearances for FC Midtjylland this season; playing a prominent role in the club securing the Danish Superliga title with two games to spare.
In total, Haugaard made 35 appearances for the Wolves following his switch from league rivals Akademisk Boldklub in 2012.