"It was a huge factor," Broadfoot told www.rangersfc.co.uk. "I got offered a contract a few months ago when Walter's own future hadn't been resolved and I said no straight away."
He added: "The fact I didn't know who the manager was going to be made it hard to stay but now we know it will be the gaffer, that's huge for everyone at the club.
"He commands so much respect and I've enjoyed working with him over the last three years.
"With Ally McCoist going on to be the gaffer too next summer, it was really attractive for me to stay and work under them both."