The midfielder has signed a three-year deal after leaving the Blades on a free transfer.
The former Everton trainee rejected a new contract offer from the Blades after playing 120 times in four years at Bramall Lane and Gerrard’s pitch helped the 27-year-old choose Ibrox to continue his career.
The boyhood Liverpool fan said: “I spoke with the manager and he sold the club to me, and I was just taken aback by his ambition, vision and drive.
“I know Glasgow is like Liverpool – a proper football city with proper football fans, and I know the people are very similar and I am buzzing to be a part of the atmosphere I am moving into.
“The chance to work with Steven Gerrard and Gary McAllister, as well as Michael Beale, was a huge draw.
“The manager is from the same area as me, and I want to learn from those coaches and become a better version of myself and continue to develop under them.
“As an outsider looking in, the scenes last season were unbelievable when the club won the league, and when I saw that, I knew I wanted to be a part of it and be a part of a club which wins more trophies for Rangers.
“There is something special still being built here and there is more to come. The pull of being in the Champions League was also massive for me.”
Gerrard has been a long-time admirer of the former England Under-20 international.
“John is a player I have known for some time and knew he would enhance our squad,” the former Liverpool captain said.
“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. He 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.
“Myself and the staff are looking forward to working with John. We know he is also very excited to get started at Rangers.”