Aksalu has been on several trials at the Shirecliffe training facility over the past two months where he has trained with goalkeeping coach Andy Learning.
Blades manager Kevin Blackwell was pleased with the signing and told the club's official website: "He has proved to be one of the best goalkeeping trialists we have seen for a long time.
"It's a terrific opportunity for him and if he continues his development he will become the number one Estonian goalkeeper.
"We are hoping he can fulfil his undoubted potential with Sheffield United and cement his international career."
Source: Team Talk
Source: Team Talk