The 20-year-old Northern Ireland ace made the move to Rangers from Linfield in 1997, but his career has stalled in Glasgow and he now hopes to make an impression at Tannadice after signing a three-year deal.
"I enjoyed my time at Ibrox," the winger said. "But there were few opportunities for me there and I am ready to take my chance here.
"It is another chance to play in the SPL, and United appear to be going places."
United manager Alex Smith expressed his delight at finally sealing the £150,000 capture, after having had bids rejected earlier in the year.
"Steven wants first-team football and while a starting place is not guaranteed here, I have told him he will get his chance with Dundee United," said Smith.
"He can play anywhere in the front-line and can add to our attacking options, especially as he is adept at supplying crosses.
"Steven is an ambitious lad and at 21 is coming to Tannadice at a good age. He's the type who recognises that there is life after Rangers - his new team-mate Charlie Miller can testify to that."
Meanwhile, Jamie Fullarton has revealed that he is close to a return after recovering from the broken ankle that sidelined him for much of last season and the groin strain that has hampered his pre-season efforts.
He said: "I missed most of last season but I`m desperate to get involved, the ankle is now perfect."
