The goalkeeper signed permanently from West Ham this week. Trott has spent the past two seasons on-loan with Vejle.
He said, "I am very satisfied with the season I have just had. But now I think it's time for the next step.
"It is the right time to try something new in my career - in the form of chasing trophies. I want to raise my standards and be part of a team that is expected to win every single time.
"It feels good to receive interest from FCK. It is the highest form of recognition you can get in Scandinavia."
He added, "It has been really easy for me. The boys and the staff have been good to me. They have given me room to adapt both in and out of training. There is a good atmosphere here.
"Everyone treats everyone the same, and they talk to me as if I've been here for many years, and I really like that.
"It's a good team and a good group of boys, concludes the keeper."