"I had another year of my contract to run but I'm ambitious and I want to be playing first team football," the 26 year old said.
"I felt that I did well during my time at Ibrox but they had guys like Allan McGregor and Roy Carroll and then Neil Alexander on their books - all international goalkeepers and it is hard to get ahead of keepers of that quality.
"It was a great experience and I am definitely a better goalkeeper now than when I signed for Rangers but it is time to move on and try and get myself playing regularly in the SPL the way I was when I was with Kilmarnock."
Smith has no regrets about time he spent at Rangers, adding: "It was a great experience.
"To be on the bench for the UEFA Cup semi-finals and final and then the Scottish Cup final against Queen of the South was something I won't forget.
"It has given me a couple of notable medals as well which are nice to have but as an unused sub you don't feel you have earned them.
"There is nothing better than feeling you have earned success and that is what I want to do."
Saints are back in the top flight following an absence of seven years after clinching the Irn-Bru First Division title last season.
Smith told www.perthstjohnstonefc.co.uk: "I only heard about St Johnstone's interest late last week.
"I spoke with Derek McInnes and I liked the sound of his plans for the team and what he wants to do.
"He didn't state whether he envisages me as being the first, second or third choice keeper, just that he wants a strong squad and that it is up to me to do well and try and force my way into the team.
"I can't wait to meet up with the boys next Tuesday and get started. Rangers only came back to training on Thursday so next Tuesday will be the start of my pre-season training and I can't wait."