The Sweden international joined United on loan from Roma at the end of the summer transfer window but poor form on his part and that of the team generally under Slavisa Jokanovic made it a signing that both parties would probably come to regret.
A series of notable errors – the first coming as early as his debut in the 2-2 draw with Preston at Bramall Lane – meant he was never taken to by Blades fans.
Olsen picked up an injury while on international duty in mid-November and hasn’t played since.
It had been rumoured for over a week that Villa were interested in the keeper and upon cutting short his deal with Roma, Olsen was confirmed as a Villa player on a temporary basis on Tuesday afternoon, following on from Steven Gerrard taking Philippe Coutinho on loan to Villa Park last week.
After the move was confirmed, Olsen said it was an ‘easy’ decision to join Gerrard.
“I’m really, really happy,” he told Villa’s website.
“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.”
He added: “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.”
He said: “When you come to the car park and see the building (at Bodymoor Heath), 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.