Smith worked with Murray for four years before the Scot moved to Spain, but he has insisted that it has taken a "huge amount of work" for the 26-year-old to become Wimbledon champion.
The Great Britain Davis Cup captain told BBC Sport: "We always saw that there was a champion in the making throughout his entire junior tennis career.
"He was always at the top end of the international stage. But it takes a huge amount of work to get from that point to being Wimbledon champion."
Murray become the first British winner of the men's singles title at Wimbledon in 77 years when he defeated Novak Djokovic in yesterday's final.