The 43-year-old gained recognition after leading Ostersunds from the Swedish fourth-tier to the top-flight in seven years at the club. He also guided them to the last-32 of the Europa League last term, where they were knocked out by Arsenal.
Potter replaces Portuguese boss Carlos Carvalhal, who left Swansea after the Welsh club’s relegation from the Premier League last season.
“It’s a chance to start again,” Potter told Swansea’s website. “We know how frustrating the last few years have been, but hopefully the relegation will be seen in a few years’ time as the best thing that ever happened to the club.
“We will try our best and work hard every day to give the supporters a team they can feel proud of; they can connect with and see are trying to improve.”
The former Southampton and Stoke City defender will be joined by assistant Billy Reid and recruitment analyst Kyle Macaulay at the Liberty Stadium.