The centre-half has made just one competitive appearance for the club since first arriving at Ibrox in January 2007.
But Webster, whose injury problems with Rangers began when he damaged knee ligaments in his first training session, revitalised his career last season.
The 28-year-old resumed his Scotland career after a four-year absence, won a Scottish Cup winners' medal and made the shortlist for the PFA Scotland player of the year award.
"Although I have finally overcome my injury problems and got back playing week in, week out during my spell at Dundee United, I have a huge amount to thank everybody at Rangers for," Webster said in the Evening Times.
"They are a great bunch of boys and have really helped me through the darker times.
"When I was out of action and doubted I would get back playing on a regular basis at a decent level they definitely kept my spirits up.
"The Rangers boys welcomed me with open arms and made me feel part of things. They have kept in touch with me when I moved on to United on loan to see how I was getting on. Their support has been important."
He added: "I moved to a big club like Rangers to elevate my career to a new level and, thus far, I have not been able to do that.
"But there is the opportunity for me to do that now and I will relish the opportunity to get back into things."