The Norway international midfielder spent five years at Manchester United where he worked with former Old Trafford reserve coach Solskjaer.
The 23-year-old, who never made a first-team appearance for United, became Solskjaer's first signing when joining from Heerenveen for a reported £2m fee.
He goes straight into the squad for Saturday's home game against West Ham, Solskjaer's first league game in charge since replacing Malky Mackay last month.
"It was an easy decision when I head Heerenveen had got an offer from Cardiff. It was a no-brainer really and I went as fast as I could," said the former Molde player.
"The lads are great, they have taken good care of me, training has been really good and it is really a step up for me."
Eikrem was part of two league successes under Solskjaer and is looking forward to forging another successful partnership with the former United striker at Cardiff.
"I saw what type of manager he was at Molde. The focus was the same all the time, it was about getting us playing again and getting everyone excited to play," he said.
"When we were struggling at the bottom of the table he just said how good players we were and just continue how we did last year."