The 32-year-old Sweden international has agreed to join on loan for the rest of the season.
Olsen, who has 53 caps for his country, will provide experienced back-up to No.1 Emi Martinez.
He joins Villa having spent the first half of the season in the Championship with Sheffield United, where he made 11 appearances before sustaining an injury in November.
“I’m really, really happy,” said Olsen. “It’s been a couple of days of waiting to come here, so when I woke up this morning and I knew I was signing for the club I was really happy.”
“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. It was an easy choice from the first call I had from my agent.”
Olsen, who made seven Premier League appearances while on loan at Everton last season, becomes Villa’s fourth signing of the month following the arrivals of Philippe Coutinho, Lucas Digne and Kerr Smith.
“When you come to the car park and see the building (at Bodymoor Heath), you see that it’s a massive club,” said Olsen.
“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.”