The Nottingham Forest centre-back has not featured in the Premier League since September and his only recent club action was off the bench in extra-time in an FA Cup win over Blackpool.
The 27-year-old was reported to have been frozen out of the first-team picture amid a contract dispute with his Forest deal set to expire in the summer.
The move to the Danish side, who are set to face Manchester City in the Champions League last 16, will boost McKenna’s hopes of being in Scotland’s Euro 2024 squad.
“FC Copenhagen are an internationally-respected club who play for the titles every season and who have done fantastically well on the international stage.
“I’m really looking forward to meeting the team and joining the training camp, which is a perfect starting point for me in terms of getting into the group quickly.
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