Rohl, who led the team to a 12th-placed finish last season, had looked set to leave last month when he did not return to take pre-season training but eventually came back in early July, only to leave by mutual consent on Tuesday.
Pedersen has previous managerial experience across Europe in his native Denmark, as well as in Germany and Norway.
“I am incredibly, incredibly proud to become manager of this wonderful football club,” he told the club website., external
“Since arriving in Sheffield with my family, the city immediately felt like our home.”
He added: “Is this going to be easy? No! We are maybe in ‘rough waters’ at the moment but as a proud Dane I can tell you that like our Viking ancestors, stormy seas don’t bother us too much. You have to get used to it, to weather the storm to get to calmer waters.
“To the fans, I ask that we stick together. At times we may need to be a little patient as we strive to grow. We all care deeply and will do all we can to bring the great times back to Hillsborough.
“I only ask that you get behind your team.”
