Potter signed a three-year contract with the Championship side on Monday following his exit from Swedish club Östersund.
MEMBERS' QUIZ: Test your knowledge of Sweden at the World Cup
The 43-year-old replaces Carlos Carvalhal, who was sacked after a dismal campaign ended with Swansea's relegation from the Premier League on the final day of the season.
“I understand the frustration and disappointment following relegation. It's the same for every football club in the world when you go down,” Potter told Swansea's website.
“There are a lot of similarities with Östersunds and Swansea. It's about trying to build a football club identity that people can be proud of and can connect with.”
Having sealed a move that was first agreed last week, Potter arrives to find a club in need of a lift after a turbulent period that saw his predecessors Francesco Guidolin, Bob Bradley, Paul Clement and Carvalhal all fail at the Liberty Stadium since January 2016.
The Englishman has earned a reputation as a talented young coach thanks to his work in eight years at tiny Östersund.
He lifted them from the fourth tier in Sweden to the top-flight with three promotions and a Swedish Cup triumph.
Potter led Östersund onto the global stage this season as they competed in the Europa League, reaching the last 32 before losing 4-2 on aggregate against Arsenal — a tie that included an impressive 2-1 second leg victory at the Emirates Stadium.
His managerial rise came after a modest playing career in England as a defender with Stoke, Birmingham, Southampton and West Bromwich Albion among numerous clubs.
Potter knows he faces a tough task to maintain his ascent with Swansea, but he hopes building a more unified atmosphere will be a step in the right direction.
“The last two or three years have been a battle to stay in the Premier League, which is an unforgiving competition. Now we need to move on,” he said.
“All the times I've experienced Swansea City over the years, especially when they were successful, there's not only been a clear playing style but also a feeling of togetherness at the club.
“We are not miracle workers, just down to earth people that will try hard to create something people will be proud of.”