Former Manchester United midfielder Eikrem impressed at the recent European Under 21 Championship for Norway and had been linked with several clubs in the Bundesliga.
However, he has opted for a four-year contract with Heerenveen and the Dutch club are delighted to have signed the 22-year-old.
Technical director Johan Hansma told the club's official website: "Magnus is a very talented midfielder, an all-rounder with a good pass and technique.
"He played during the European U-21 Championship in Israel and was one of the most important players at Norway U-21s who were beaten by Spain U-21s in the semi-finals.
"We tracked Magnus for a long time and there was also serious interest from Germany. Therefore we are very proud he has chosen us."
Eikrem had earlier acknowledged that his decision to join Heerenveen was swayed by the presence of Marco van Basten as the club's coach.
"There is a strong desire from the coach [Van Basten] that I should go down there," said Eikrem.
"It is tremendously important that it is the coach who wants me and not the sports director or something."
Meanwhile, Dutch wide-man Wildschut has agreed a three-year contract with Heerenveen, with the option of a further two seasons.