The former Newcastle and Southampton left-back had been training with Wanderers for a fortnight and had even passed a medical but opted to move north of the border on transfer deadline day.
"I know Bolton wanted to sign me but this is a massive club," he said.
"I also have the chance to play Champions League football. That is important to any player.
"I played a lot of European football when I was at Newcastle and I hope to do the same at Rangers.
It was an easy decision."