Falk won five Danish Superliga titles, three Danish Cup finals, and played a significant role in three Champions League campaigns during his time in Copenhagen.
He scored 29 goals and provided 49 assists, having joined the club from OB back in 2016.
Discussing the end of the Copenhagen chapter of his career, Falk says: "It has been a huge honour to play for F.C. Copenhagen. The club has meant everything to me over these years, and I feel privileged to have been part of so many great experiences."
"To be allowed to play in the Champions League, win titles, and feel the atmosphere in Parken – that is something I will never forget. I have developed enormously as both a player and a person, and my family and I take many strong memories and relationships with us."
"There are many people that I have met during my time at F.C. Copenhagen, and whom I will hug when I see them – but first and foremost, they should be thanked for making my time at this club something I will never forget.
"Now it is time to be closer to my family and take the next step with OB, where I had some good years before moving to Copenhagen.
“I will always carry the club in my heart and follow from the sidelines. F.C. Copenhagen will forever be an important part of my life.”
FCK head coach Jacob Neestrup adds, “For nine years, Rasmus has been the player who has helped to create a bridge between new players and new coaches."
“With his great playing intelligence, he has delivered some fantastic performances in the F.C. Copenhagen jersey. Performances at the absolute highest level to the great delight of fans, coaches, and many others. He has been a crucial player for many years for F.C. Copenhagen.