Both parties have agreed a deal for the Scotland B international for a price of £500,000 which could rise to £800,000.
He has been sold for more than what United bought him. He joined the Blades for £100,000 from Oldham and has had his fair share of injuries, highs and lows and has finally made his may to Berkshire.
The left-back had been pushed out of the first team due to Gary Naysmith showing good enough performances to stay in the team. Blackwell on the sale said:
"I didn't have any intention of letting him go but the offer came in and, with his immediate chances of a first-team place a bit limited, I didn't feel it proper to deny him the chance of a good move for him.
"Looking at our squad I feel that for the first time in my managerial career I can actually build a team whilst I already have a good one, because of the quality of this squad.
"With previous clubs I have had to sell first before being able to bring somebody in which makes things a lot more difficult. Now I have the luxury of controlling when players leave to a large extent."
On the move to the Madejski Armstrong said: "It was definitely an easy decision to come to a club of this size and when I came down I definitely wanted to come here."