AS says an agreement is in place over a fee for the Iceland international.
Meanwhile, Finnbogason commented: "I feel really good and I'm very happy to have signed for Real. I really want to get to train with my new teammates."
He added: "They showed great interest in me, and that's really important for a player. What I perceive for Real is that it is a big family, and you see it from the moment you arrive."
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