The defender joins his new team after completing his stint with Chinese outfit Nei Mongol Zhongyou.
Born in Sa Pobla, Spain, Crespi started his career with Spanish side Mallorca before joining Elche, Granada and Xerez on loan.
The defender then moved to Racing Santander in the Spanish top division in 2013 where he spent six months before joining CE Sabadell FC in Segunda B.
The 31-year also represented the Spanish National Team in the U-19 and U-20 category.
The Segunda B winner becomes the fifth foreign signing of the club and will join the team in Kolkata for pre-season later this week.
"I am really looking forward to this new challenge. It was a simple decision for me to move once Josep Gombau called me and explained his plans with Dynamos. I am hoping I can add a lot to this side," Crespi said.
"He is a defender who fits in perfectly into our style of play and we are happy he has agreed to join us. He adds a lot of experience to this side and having played in China will definitely help Crespi adapt to the conditions here as well," Head Coach, Josep Gombau said.
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