Davidson was in the fifties to the best amateur tennis players in the world and in 1957 performed as number 3 in the world rankings. Overall, he won 1949-1960 21 single titles. For Sweden, he played 86 Davis Cup matches and 62 of them could decide for themselves.
The highlight of his career was the year 1957 when he won the men's singles at the French Championships in Paris. He defeated in the final of the Americans Herbert Flam. In the same year he won the Rother tree in the Hamburg International German Tennis Championships. In 1958 he won together with Ulf Schmidt the doubles competition at Wimbledon.
After his career Sven Davidson worked as a TV commentator.
In 2007 he was inducted into the International Tennis Hall of Fame.