The Iceland international joins La Real for €20m.
FCK chief Sune Smith-Nielsen said, "The sale of Orri is another good proof of the very strong work that is carried out in FCK Talent every day.
"It is also an expression of the fact that we as a club can give talented, young players the playing time they need, so that they can develop and make themselves attractive - even to even bigger clubs.
"It is a sale that gives rise to several emotions at the same time. On the one hand, we are very proud to have succeeded again with a really nice development and transfer of a great talent. However, we would have liked to have kept Orri a little longer. That is also the reason why we have rejected the many offers that have been made for Orri this summer."