Eikrem, who becomes City boss Ole Gunnar Solksjaer's first new arrival since he succeeded Malky Mackay as manager, has joined the Bluebirds for an undisclosed fee from Dutch club Heerenveen.
Eikrem, 23, is a former Manchester United youth team captain.
Solskjaer told Cardiff's official website: "I've known Magnus for many years, having worked with him at Manchester United and then signing him for Molde.
"While I was there I had to sell him as he was our best player - and now I feel lucky to get to sign him again for Cardiff City for a reasonable price. I see this as money well spent.
"He's a playmaker, a quarterback if you will, someone who likes to get on the ball and can see a pass.
"He is technically very good, including set-pieces, and has great vision. Magnus will add a lot to Cardiff City and will blend in very well with the midfielders in the squad."
Eikrem watched Cardiff's FA Cup third round victory over Newcastle last Saturday and he has trained with the squad this week while waiting for the necessary clearance.
Molde-born Eikrem was signed by United on his 16th birthday and he made his first team debut in 2007, going on as a substitute for Ryan Giggs in a pre-season friendly against Dunfermline.
He moved to Molde, under Solskjaer's management, in 2011 and enjoyed title success with them before joining Heerenveen last summer.
Eikrem made his Norway debut two years ago and has so far won more than a dozen caps.