Cardiff sack Solskjaer
The Championship club announced the decision on Thursday and will replace the former Manchester United forward with Danny Gabbidon and Scott Young for their trip to Derby County this weekend.
Cardiff - relegated from the Premier League after finishing bottom last term - have made a poor start to the season.
Tuesday's 1-0 home defeat to Middlesbrough left them 17th in the table with just eight points from seven matches.
Cardiff chairman Mehmet Dalman said, "Having spoken with Ole on deciding the best course of action for all parties, I'm sorry to say that we have agreed that it is in the best interest of the club for us to go our separate ways.
"Ole has been a wonderful professional to work with since his arrival at the Club. Due to a difference in philosophy of approach to the game, we have decided to part company amicably. He and his family will always be welcome at Cardiff City. I know I have gained a good friend whom I wish well and remain confident in his future success."
Solskjaer arrived at Cardiff to much fanfare in January after guiding Norwegian club Molde to two league titles in just over three years.
But Malky Mackay's replacement was unable to preserve Cardiff's top-flight status in their first ever Premier League season.
And Solskjaer himself took the responsibility for Cardiff's sloppy start to this season, saying after Tuesday's loss: "I'm responsible and I should get better results than what we've had in the first seven games."
Rumours suggested Cardiff were interested in persuading Dundee United manager Paul Hartley to replace Solskjaer.
However, the Scottish side moved quickly to end speculation.
A club statement read: "The club would like to confirm that manager Paul Hartley has long-term plans to stay at Dundee.
"As a club, we are not surprised that speculation linking Paul to other clubs has come up due to the fantastic job he continues to do at Dens Park."