The 22-year-old Denmark international, who had a contract with Aalborg until June 2015, will transfer immediately, the club said.
"Kasper's departure leaves a gap, but we have said goodbye to other players before and got through it and I am sure it will happen again. Others will now get a chance," AaB sporting director Allan Gaarde said in a statement.
The sale does not change the club's earlier announced financial outlook for 2014 of a profit about 13 million Danish crowns (1.38 million pounds).
Twente, third in the Dutch first division championship, are taking part in this season's Europa League.
(Reporting by Annabella Pultz Nielsen; Editing by Rex Gowar)
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