Crespo made his River Plate debut and scored 13 goals in 25 league matches in 1993/94 season. He helped River Plate win the Apertura league title, the second of two championships held in Argentina in the year. He helped River win the Apertura title again in 1994.
In February 1995, Crespo won his first cap for Argentina, in a friendly against Bulgaria in Mendoza, but he had to wait 16 months for his second cap and more than two years for his first Argentina goal.
In 1996, Crespo helped River to win the Libertadores Cup, the South American club championship, scoring twice in the home leg of the final in Buenos Aires.
He left River for Parma A.C in Italy in August 1996 after he won the Olympic silver medal with Argentina team at Atlanta Games, finishing the tournament as top scorer with six goals.
In May 1997, Crespo helped Parma finish runners-up in Serie A, scoring 12 goals in 27 matches.
In 1999, scoring the opening goal in 3-0 final victory over Olympique de Marseille in Moscow, Crespo helped Parma to win the Italian Cup and the UEFA Cup.
He ended his Parma career in 2000 and broke the world transfer record when he signed for newly crowned Italian champions S.S. Lazio for $54.1 million. He ended his first season in Lazio as top scorer in Serie A with 26 goals.
In September 2002, Crespo signed for Internazionale as replacement for the departed Ronaldo, joining for $40 million euros.
He signed for Premier division football club Chelsea F.C on 26 August 2003.
Fans called Crespo "Valdanito" (little Valdano) after 1986 World Cup winning forward Jorge Valdano because of his similar looks, build and running style to Real Madrid's present sporting director.