Cornelius arrived in south Wales on a five-year deal at the beginning of July in a club-record transfer, believed to be worth around £8million.
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However, he was unable to gain regular first-team football with his only starts coming in the FA Cup.
The 20-year-old will now seek to relaunch his career on familiar soil, having scored 18 league goals for Copenhagen last season.
A statement on the Danish club's official website reads: "FC Copenhagen have re-signed the club’s former top scorer, Andreas Cornelius, from Premier League side Cardiff City.
"Cornelius has agreed a five-year contract with the Lions and transfers with immediate effect."
Expressing his relief at the move, Cornelius added: "I didn’t have a second of doubt that this was where I wanted to be, especially with the situation as it was in Cardiff.
"I have nothing bad to say about the club or anyone connected with it but I need to play football.
"I do not see it as a backwards step to play for the biggest club in Scandinavia. I feel there are many things I have not achieved with FC Copenhagen and I will definitely fight to be part of what is being built at FCK right now."