Corretja was born in Barcelona, and first came to the tennis world's attention as a promising junior player who won the Orange Bowl 16s title in 1990. He turned professional in 1991 and won his first top-level singles title in 1994 at Buenos Aires. His first doubles title came in 1995 at Palermo.
In 1996, Corretja faced Pete Sampras in an epic five-set quarterfinal match at the US Open. Pete Sampras threw up in the fifth set tiebreak, where Corretja held a match point later on, but he eventually lost to Sampras on a double fault in 4 hours and 9 minutes 6–7, 7–5, 7–5, 4–6, 6–7(7–9).
In 1997, Corretja captured three titles, including his first Tennis Masters Series title in Rome, where he defeated Marcelo Ríos 7–5, 7–5, 6–3. (He won a second Masters Series title in 2000 at Indian Wells.)
1998 saw Corretja reach his first Grand Slam final at the French Open. In the third round, he defeated Argentina's Hernán Gumy in (at the time) the longest match in the tournament's history. Corretja won the 5-hour 31-minute marathon 6–1, 5–7, 6–7, 7–5, 9–7. In the final, Corretja lost to fellow-Spaniard Carlos Moyà in straight sets 3–6, 5–7, 3–6.
Corretja finished 1998 by winning the most significant title of his career, the ATP Tour World Championships (now known as the World Tour Finals). In the semifinals, he saved three match points on the way to beating Sampras 4–6, 6–3, 7–6. In the final, Corretja faced Moyà in a five-set marathon and came back from two sets down to win in 4 hours and 1 minute 3–6, 3–6, 7–5, 6–3, 7–5. Corretja's win made him the first man to ever win the Tour Championships without having ever won a Grand Slam tournament (David Nalbandian, Nikolay Davydenko and Grigor Dimitrov have since repeated the feat.)
In total, Corretja won a career-high five singles titles in 1998 and finished the year ranked world no. 3. This year Corretja won in Lyon, played on carpet, a "damned" surface for Spanish tennis in the 90's. This year also won in Dubai (hard court), defeating countryman Felix Mantilla. These results, joining with the good results on clay, made Corretja the most versatile Spanish player for several years. In February 1999, Corretja reached his career-high ranking of world no. 2.