Potter, who has previously coached several Premier League clubs such as Chelsea, West Ham and Brighton, has been given a short-term contract that includes Sweden's possible playoff games in March next year.
However, the contract will be automatically extended if Sweden qualifies for the World Cup.
"I am very honoured by the task, but also incredibly inspired. Sweden has fantastic players who deliver in the world's best leagues week after week. My task will be to create the right conditions so that we as a team can perform at the highest level and lead Sweden to the World Cup next summer", said Potter, who will start the work from today.
The Englishman, who has a past as a coach in Swedish football, takes over a team that has been a huge disappointment in the World Cup qualification.
Under Tomasson, they only gained a single point in four qualifying games, and this means that they are currently a long way from the World Cup, six points adrift from second place with just two games to go.