The 29-year-old joins for an undisclosed fee on a two-year deal, with the option of a further 12 months, following Wigan’s relegation to League One.
He will compete with Kelle Roos and last season’s No 1 Lee Grant for a first-team place.
Head coach Paul Clement said: “Competition for places across the squad is important and Scott’s arrival certainly brings that to the goalkeeping department.
“We have two good goalkeepers already, and bringing Scott in will certainly raise the battle for the place between the posts.
“Scott is an experienced goalkeeper who has played at the highest level for a number of years and we’re looking forward to working with him.”
Carson, who has four England caps, is Derby’s third summer signing following deals for Alex Pearce and Darren Bent.
“This deal has happened really quickly and it’s good to get it all boxed off,” he said. “I’m looking forward to getting started and everyone knows Derby County is a massive club, so I was delighted when I heard that there was interest.
“I want to play at the very highest level and get back in the Premier League. Speaking to the head coach and the people at the club, they have the same desire as well. That was one of the main reasons that I wanted to get the deal done.”