"I am incredibly proud to be a part of Everton," the 41-year-old Sørensen told the club's website.
The Dane is taken from Fortuna Hjørring, which he led to two league titles in 2014 and 2016.
Big-bet Everton have had a turbulent season and are ten out of twelve teams in the English top division Super League after 19 games played.
The goal was to finish in the top three, but after a heavy start to the season, coach Willie Kirk had to leave his post.
The Frenchman Jean-Luc Vasseur took over, but could not reverse the trend and was fired after only ten matches.
The Swedish star trio Björn, Bennison and Anvegård were recruited to the Liverpool club before this season and will meet their future coach as early as next week.
Sørensen will then get acquainted with the management staff and the player squad, but he will not take over until this summer.
Until then, Chris Roberts and Claire Ditchburn are still acting head coaches.
Defender Nathalie Björn and midfielder Hanna Bennison are part of the Swedish national team that is currently qualifying for the World Cup.
On Thursday, it was a crushing 15-0 victory away against Georgia and one point on Tuesday against Ireland in Gothenburg is enough to secure a direct place in the World Cup in Australia and New Zealand next year.
Anna Anvegård is not selected because the attacker is recovering from a concussion.
CLIP: United defeated Everton at Old Trafford
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United defeated Everton in front of 20,000 at Old Trafford.
Photo: Bildbyrån