The 45-year-old's appointment comes just three weeks after he led modest Argentine side Defensa y Justicia to the Copa Sudamericana title.
The former striker, a Premier League winner with Chelsea and three-time Serie A champion with Inter Milan, has signed a two-year contract.
"He has a winning history, he was a great athlete and is a very promising coach," Sao Paulo president Julio Casares said.
"We have a commander with a winning mentality," he added.
Crespo replaces Brazilian Fernando Diniz, who was fired after a string of poor results that dropped Sao Paulo off the top of the Brazilian championship.
It has not won in seven league matches, losing four, including a 5-1 home reverse to front-runner Internacional.
Sao Paulo is fourth, seven points behind with four matches remaining, but needs to maintain that position to qualify automatically for the Copa Libertadores group stage.
It has a tough run-in, including matches against Flamengo, which is fighting for the title, and two sides – Gremio and Palmeiras – attempting to dislodge it from the top four.
Crespo made his name as a striker for River Plate in his homeland, where he won the Copa Libertadores in 1996 and two Argentinean titles.
He earned a move to Parma in Italy where he played in the club's glory era under Carlo Ancelotti and alongside Gianluigi Buffon, Fabio Cannavaro and Lilian Thuram.
After moving to Lazio, Crespo was one of the first players signed by Chelsea when the London club was bought in 2003 by billionaire Russian Roman Abramovich, who immediately embarked on a multi-million spending spree.
Jettisoned on loan to AC Milan a year later after Jose Mourinho took over as manager from Claudio Ranieri, Crespo scored twice in the 2005 UEFA Champions League final before Liverpool came back from a 3-0 half-time deficit to win on penalties.
Crespo returned to Chelsea the next season and won the Premier League title before collecting three Serie A crowns in a row after beginning a second spell with Inter, initially on loan.
He scored 35 goals in 64 games for Argentina – one more than Diego Maradona – and is fourth on his country's all-time scoring list behind Lionel Messi, Gabriel Batistuta and Sergio Aguero.
He began his coaching career at Modena in Italy before returning home to take over Banfield in January 2019 and then Defensa a year later.