Crespo made his debut with River Plate during the 1993–94 season, scoring 13 goals in 25 league appearances as River Plate won the Apertura league title. In 1996, he helped River win the Copa Libertadores, scoring twice in the home leg of the final in Buenos Aires.
Crespo left River Plate for Parma on 14 August 1996 after he won the with Argentina at the 1996 Summer Olympics and finished as the top scorer with six goals. He failed to score in his first six months at the club and was routinely booed, with head coach Carlo Ancelotti coming in for much criticism for keeping faith with the selection of Crespo. His faith, however, vindicated – Crespo went on to score 12 times in 27 matches in his first Serie A season and Parma finished runners-up to Juventus. The turning point was the standing applause he received for his brace against Cagliari in March 1997. Parma won the 1998–99 Coppa Italia and he scored the opening goal in Parma's 3–0 UEFA Cup final victory over Marseille. He had scored 80 goals in four seasons.
In 2000, Lazio broke the by paying £35 million (they paid £16 million in cash and transferred Matías Almeyda and Sérgio Conceição) to acquire Crespo, who in turn finished as Serie A's top scorer with 26 goals. Lazio, however, failed to defend its league title in 2001, and the following season, Crespo suffered from some injuries, while new signings Jaap Stam and Gaizka Mendieta failed to live up their reputations, following the departures of playmakers Juan Sebastián Verón and Pavel Nedvěd. Crespo was left without the attacking support he had enjoyed in 2001, but still scored a respectable haul of goals. Lazio's financial problems, however, forced the club to sell several players, and following Alessandro Nesta's transfer to A.C. Milan, speculation over Crespo's future intensified.
On 31 August 2002, Crespo, expected to shine again after suffering from injuries, signed with Inter Milan as a replacement for the departed  for a €26 million fee and Bernardo Corradi. Lazio later re-valued Corradi to €5.5 million. Inter was short of strikers after the highly rated Mohamed Kallon was injured in August, and only Álvaro Recoba and Christian Vieri, together with reserves Bernardo Corradi and Nicola Ventola, were available.
Crespo scored seven goals in three appearances, along with nine goals in 12 Champions League matches, until he was sidelined for four months by injury in early 2003.
Crespo was transferred to Premier League club Chelsea on 26 August 2003 for a fee of reported £16.8 million, however it also created a controversy in alleged false accounting.[note 1] Following the transfer, Christian Vieri, Crespo's former strike partner at Inter, claimed that the club are essentially "weakening" by selling players of such caliber. He made his league debut on 30 August 2003 as a substitute for Adrian Mutu in a 2–2 home draw against Blackburn Rovers. On 16 September 2003, Crespo made his European debut, replacing Jimmy Floyd Hasselbaink in the 2003–04 Champions League group stage, which ended in a 1–0 away win after a late goal from William Gallas against Sparta Prague. Four days later, he scored his first goals, a double, in a 5–0 away victory against Wolverhampton Wanderers. Crespo made 31 appearances (including 19 in the league) in all competitions, scoring 12 goals.
A.C. Milan (loan)
After José Mourinho took over as Chelsea manager for the 2004–05 season, Crespo became surplus to Chelsea's plans following the arrival of Didier Drogba and was loaned to A.C. Milan, as requested by then-manager Carlo Ancelotti. He scored a total of ten league goals, and scored twice in the 2005 UEFA Champions League Final in a defeat to Liverpool.
Return to Chelsea
After Chelsea's failed attempts to land a big-name striker during the summer of 2005, Mourinho needed competition for striker Didier Drogba and decided to recall Crespo from A.C. Milan, convincing him that he had a future in England. Crespo made his first return appearance in a 2–1 win over Arsenal. He scored his first league goal of 2005 against newly promoted Wigan Athletic in the 93rd minute of Chelsea's season opener in a 1–0 win, with a left foot curler into the top corner from 25 yards. The 2005–06 league title was Crespo's first league title victory in European football.
Return to Inter Milan
Second spell; loan from 2006 to 2008
Crespo with Inter in 2007.
Though he scored 13 goals in all competitions and won the 2005–06 Premier League, Crespo requested a return to Italy in order to rejoin A.C. Milan, but Chelsea refused and announced that Crespo would remain a Chelsea player until the club accepted a suitable offer for him. On 7 August 2006, Crespo joined Inter on a two-year loan. He scored his 125th Serie A goal against Siena on 2 December 2006, and his 200th career goal in Europe on 2 April 2007. On 13 May, Crespo scored a hat-trick to help Inter defeat Lazio 4–3 and win the Scudetto. Two days earlier, he had appeared in training without his customary long hair, which he had grown out for over five years.
In scoring a Champions League goal with Inter, Crespo became the first player to score with five teams in the competition, doing so with each of the sides he had played for since moving from South America to Europe in 1996.
Third spell; permanent deal
Crespo was released from Chelsea on 3 July 2008, following the expiration of his contract, and was signed by Inter on a one-year contract for free. In the 2008–09 season, under José Mourinho, his former manager in Chelsea, Crespo only made 13 Serie A appearances, including two starts. He was excluded from the Champions League squad.
Following the expiration of his contract at Inter, Crespo was quickly snapped up by Genoa, taking Diego Milito's place, who moved in the opposite direction. On 8 June 2009, it was reported that Crespo had a medical check to formalize his transfer. Crespo cited his ambition to make the Argentina 2010 World Cup squad as one of his key reasons for making the move to Genoa. On 13 September, Crespo scored his first goal of the 2009 season against Napoli.
Return to Parma and retirement
In January 2010, Crespo returned to Parma after the club agreed the deal with Atalanta and Genoa. Crespo replaced Nicola Amoruso who left for Atalanta, while Atalanta's Robert Acquafresca moved to Genoa to replace Crespo. The Argentine striker returned after ten years to Parma. Crespo scored just once before the season's end, against Livorno. The striker enjoyed a more successful 2010–11 season, scoring 11 goals. In doing so, he became Parma's top scorer for a fourth time, which remains a post-war club record. Despite mounting speculation of his departure, Crespo signed a one-year contract extension on 30 June 2011. However, a lack of first-team opportunities saw Crespo and Parma mutually agree to terminate his contract on 2 February 2012, although he did vow to return to the city he had fallen in love with. He is the club's all-time record goalscorer with 94 goals in 201 appearances.
Although Crespo was signed to play in Bengal Premier League Soccer in late January 2012, with a salary of £533,000 for the two-month tournament, the competition never got underway. He clarified that his career as a footballer had finished in November 2012.