The defender capped an impressive campaign at Tannadice by lifting the Active Nation Scottish Cup along with his predecessor as captain, Lee Wilkie.
Webster also resurrected his Scotland career after a four-year absence during which his progress was derailed by contract disputes and a succession of injuries.
"My year at United has been incredible and one I'll never forget," the 28 year old told Rangers' official website.
"I needed to get back playing regularly again and going to Tannadice allowed me to do that.
"I wanted people to start talking about me as a footballer - pure and simple - and I hope that can now continue.
"I'll enjoy a few weeks' holiday with my family and then go back to Rangers early and in July ready to make an impact.
"I won't be nervous or apprehensive - I'm looking forward to it.
"I always felt part of things at Rangers even when I was out of the team and in the past week I've had a lot of messages from guys at the club.
"Davie Weir texted me and I've spoke to Kevin Thomson and Lee McCulloch too.
"Ally McCoist called me on the morning of the cup final to pass on his best wishes and that meant a lot too."