The ex-Blade has signed a three-year deal with the Scottish champions, linking up with boyhood hero Steven Gerrard in Glasgow after officially leaving the Blades this summer when his contract expired.
Gerrard said that Lundstram “will add steel and presence to our midfield along with his quality which makes our squad much stronger, and to procure a player of John’s profile and experience is very pleasing.”
And Ross Wilson, Rangers’ sporting director, added: “John was a major transfer target as part of our squad plan this summer so naturally I am delighted that he becomes a Rangers player today.
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"We quietly worked hard at this deal in the background whilst understanding there was a lot of competition for his signature. John has long been admired by Steven and there’s no better judge of a midfield player in my book.
"His desire to make John a Rangers player will have been a massive plus in John’s decision making I am sure. We know John’s qualities and we know that in joining our team, with the quality we already have, his game will elevate further still.
"He will particularly relish playing in the style of Rangers team that we have and playing in front of our huge fan base is an exciting prospect for him. He joins at a time where we believe at 27 years old his peak years will be with us at Ibrox.”
Lundstram grew up as a Liverpool supporter, despite coming through the ranks at their city rivals Everton. He joined United from Oxford United and played 62 times in the Premier League in Blades colours, before leaving after failing to agree a new deal.
“John is a player I have known for some time and knew he would enhance our squad,” Gerrard added.
"Having played in the Premiership, he has the undoubted quality to enhance our midfield with his technical ability and physicality and I was impressed with his attitude and ambition when we spoke over recent weeks. John is a winner and knows what is required to succeed at a club of this stature.”