The Swedish international signed a pre-contract with Gothenburg earlier this month after falling out-of-favour at Everton.
Alexandersson was set to remain at Goodison Park until the end of the season, but Toffees boss David Moyes is willing to let him leave now as he does not figure in his first team plans.
"Niclas Alexandersson left the club yesterday to return home to Sweden," Moyes told the club's official website.
"He has signed a pre-contact agreement with Gothenburg and we are allowing him to leave Everton early.
"I'd like to take this opportunity to thank Niclas for his contribution to the club, particularly during my early days here when he played a big part in helping us to avoid relegation.
"It's been difficult for him in the last 16 months or so, but we wish him and his family well on their return to Sweden."
