The left-back, 24, will become Paul Lambert's third summer signing at Norwich City when he joins as a free agent on 1 July after agreeing a two-year deal.
Lambert, of course, enjoyed a successful spell as captain of Celtic but the former Ibrox player insists his new manager's background makes no difference to him at all.
"That's not a problem," said Smith. "A few people in Scotland might think it's a problem but it's not a problem to me. I'm just looking forward to getting the season under way and I'm raring to go."
In fact, Smith cites Lambert as one of the reasons behind his switch to the Canaries as he bids to steer his career back on track after his time at Rangers was marred by a lengthy spell on the sidelines with groin problems.
Smith said: "When I met him, he was really positive and that's a big thing for me. I've not played a lot in the last couple of years and the chance to come back and rebuild my career is a big thing for me. The manager had that faith in me to bring me here and I want to repay that."
Speaking of his injury problems, Smith added: "It was two or three years ago and I was out for a long time and then there was a change of manager.
"When the new manager (Walter Smith] came in, I wasn't fit and he was really successful and it's hard to get into a successful side. I played a bit under him and I was lucky enough to win a few medals at the end of both seasons.
"I enjoyed my time at Rangers but it's time to move on. It's a new challenge and it's something I'm looking forward to."
Smith admits it is a wrench to leave the Scottish champions, having come through the youth ranks at Ibrox, but says his time at Rangers will more than prepare him for life in the Championship.
"I grew up there and I've been there since I was ten years old," he added. "I played in some big games – I played in the Champions League, big Old Firm games and games that can win you leagues. It's an experience.
"I might not have played a lot of games in a career but the games I've played in can stand me in good stead for playing in this league.
"It's a big challenge. I don't really need to prove anything to myself. People always put question marks over you because of the injuries but it's not something I'm worried about.
"I just want to play football again and get a regular run in the side and show people the levels I know I'm capable of reaching.
"I know a lot of boys who have played in the league who have come from Scotland. It's a good league and it's very competitive so it's a big challenge."
Meanwhile, Lambert himself also committed his future to Norwich by signing a new contract along with his coaching team Paul Culverhouse and Gary Karsa.
Norwich were also ordered by a Football League disciplinary commission to pay Colchester 425,000 in compensation over the appointment of Lambert and his team.