The Argentine has moved on a free transfer to Inter Milan but the deal allows Chelsea the option to take him back to Stamford Bridge after one season.
Inter sporting director Marco Branca, a Chelsea representative, Crespo and his agent Fernando Hidalgo met in Milan on Monday to finalise the move.
Crespo, 31, recently acquired Italian citizenship and had made no secret of his desire to return to Serie A.
The forward, who has played for Parma, Lazio, Inter Milan and AC Milan, still has a house in the town of Limido Comasco, on the outskirts of Milan.
Last week he said: "The fact is I love Italy. The money and success don't come into it.
"Italy is my natural environment, it is the place where I will live when I retire and it is the best place to play."
Crespo has also attracted interest from AC Milan, with whom he spent the 2004/05 season on loan from Chelsea.
He signed for the Blues in August 2003 for a fee of £16.8m.