The 19-year-old Dane wants to get a first-team place at Arsenal after a successful season on loan at Birmingham.
He said: “It has always been my goal to get my breakthrough at Arsenal. There were no other clubs that were interesting for me.
“I know I have the right qualities, or will be able to develop them. I truly believe that I can break through.”
He added: “I have had meetings with them where they have told me that I figure in their plans for the future.
“If that had not happened, neither they nor I would have signed the deal.
“The other strikers may have an advantage over me, but when I restart training and get some good matches under my belt, I am sure I will get my chance and take it.”