The 23-year-old signs a three-year deal at the Britannia Stadium as the Potters look to replace the departing Thomas Sorensen.
Haugaard will provide competition for Asmir Begovic and Jack Butland having made 24 appearances in Midtjylland's title-winning campaign.
"We are delighted to have captured our second signing of the close season, by bringing Jakob to the club," chief executive Tony Scholes told the club's official website.
“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.”
Haugaard becomes Mark Hughes' second signing of the summer after completing the permanent capture of Philipp Wollscheid following a successful loan spell.