The Swedish goalkeeper joins on loan for the remainder of this season.
"It was easy (the decision to join Villa). When I heard about it from my agent for the first time, I decided to do whatever I could to change club and sign for Villa," Olsen told the club's official website.
"It was an easy choice from the first call I had from my agent. When you come to the car park and see the building, you see that it's a massive club.
"I've heard how good it is but when you're inside and see the facilities, it's amazing. You have everything you need to improve yourself and be as good as you can be."
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