The England Under-20 star was snapped up for a mere £100,000 from the Boundary Park club, making Neil Warnock's summer signings a total of three so far.
New £100,000 cash signing Chris Armstrong
Armstrong told www.sufc.co.uk: "I'm already feeling a bit nervous but very excited about joining such a big club that did so well last season.
"I saw United quite a bit on television and was impressed with both their football and the blend of youth and experience."
Meanwhile it has emerged that David Kelly is expected to be named as new the Blades number 2 with in the next 24 hours, also ex-Blades defender Kevin Murphy has joined Division Three outfit Kidderminster Harriers on trial.