The 24-year-old Eikrem, who has 14 caps, was among the Norwegian contingent signed by former Cardiff manager Ole Gunnar Solskjaer who found themselves surplus to requirements when the former Manchester United striker left the Welsh club.
Released from his contract in December, Eikrem will be reunited with ex-Cardiff team mate Jo Inge Berget at the southern club, who won the Allsvenskan for the second time in a row and reached the Champions League group stage in 2014.
"The reason that it was Malmo is mostly because they are the biggest club in Scandinavia at the moment, so it was quite a simple choice," Eikrem said in a statement announcing his arrival.
Malmo's success has come at a cost, however, as clubs around the world have snapped up the likes of striker Isaac Kiese Thelin (Girondins Bordeaux), midfielder Markus Halsti (DC United) and wingers Emil Forsberg (RB Leipzig) and Magnus Eriksson (Guizhou Renhe, China).
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"Magnus Wolff Eikrem is a very skilful playmaker in central midfield, and will be a good addition to the team," said Malmo's sporting director Daniel Andersson.
(Reporting by Philip O'Connor; Editing by Ken Ferris)
