Tarango turned professional in 1989, after completing his junior year at Stanford University where he won two NCAA team titles. During his career, he won 2 top-level professional singles titles and 14 doubles titles.

His career-high world rankings were World No. 42 in singles and No. 10 in doubles. He was runner-up in the men's doubles at the 1999 French Open (partnering Goran Ivaniševic').

Tarango retired from the professional tour in 2002, and is now a member of the Fed Cup and Davis Cup Committee.