Webster has started just one game since his move to Rangers in 2007 and spent most of last season out on loan at Dundee United.
Webster told the Evening Times: “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.
“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.”