The Blades announced the signing of Henderson this afternoon after the stopper extended his contract at Old Trafford until 2020.
The 21-year-old spent last season on loan at Shrewsbury Town in League One and played 48 times, including the play-off final against Rotherham United at Wembley. Henderson saved David Ball's early penalty but eventually ended up on the losing side.
"This is a big one for us, as Dean was certainly a target for rival clubs in our division," Blades boss Chris Wilder said.
"It is a position you've got to get right in terms of not only ability, but character too and we have no doubt following chats between myself, Dean and Darren Ward, that we've got both.
"Dean is a confident boy, who has proved himself wherever he has been. He is positive and most importantly a winner and he will handle the pressure of coming here.
"He had a fantastic season for Shrewsbury, playing a starring role in what they achieved last year, and he is someone we've tracked for quite a while now.
"We're well stocked now in what is a crucial department at any level and we've got very healthy competition for that number one jersey."
The move for Henderson likely ends Jamal Blackman's hopes of a return to Bramall Lane. The Chelsea youngster spent last season on loan in South Yorkshire and is known to have been keen on a return, but Henderson will instead compete with Simon Moore for the No.1 shirt when the season kicks off again in August.