The Dane said: “It has been an important decision for me to make, and I am at that stage of my career now where I wanted to make the right decision – and believe I have.
“We had been in talks for a while, without either party forcing the issue, and I said that Birmingham was the club I wanted to sign for if I was leaving Arsenal.
“I have been really enjoying my football here and hope I can play a part in getting us promoted. We are in a good position, and the club and all the players want to push on now.
“Everyone wants to play at the highest, and the style of play might suit me more in the Premiership.”