Cornelius has struggled to make an impact with the Bluebirds, failing to score in any of his 11 outings.
Speaking about his time in the Premier League, the striker told Copenhagen's official website: "I have nothing bad to say about the club [Cardiff] or any of it over there, but I need to play football.
"I do not see it as a step back, to go to the biggest club in Scandinavia. I feel there are many things I have not achieved with FC Copenhagen yet, and I definitely want to be part of what is being built at FCK right now."
It is believed that Copenhagen have paid around £3m.