Erasmus has penned a two-year deal with the second division side, ending speculation over a possible return to South Africa,
The 27-year-old was linked with several PSL clubs soon after parting ways with French Ligue 1 outfit Stade Rennes earlier this season.
However, he opted to remain in Europe and look to revive his career.
Speaking to the Eskilstuna website after signing the contract, Erasmus revealed that this wasn't an easy decision, but he sees it as an opportunity to play regular football again.
"I hope to win the love of fans through my goals. It was a difficult decision to make, but there is a good opportunity for me to play again. I have not played football for a few months so I have a lot of desire. I just want to be happy to do something that I like," said Erasmus.
The South Africa international moved to France during the 2015/16 season, but after struggling for game time in his first few months, he was relegated to the reserve teams.
Erasmus started the 2016/17 season with a bang at Rennes making eight appearances in the first half of that campaign, but his failure to score goals forced the club to loan him out to Lens where he made 12 league appearances and found the back of the net once.
Rennes recalled him for the start of the 2017/18 French Ligue 1 season, but the former SuperSport United struggled to break into the first team, and ended up being relegated to the reserve team yet again.
In Feruary this year, soon after the closing of the transfer window, Rennes announced their decision to terminate Erasmus' contract with immediate effect.