The 34-year-old will join East Bengal's ranks for the upcoming season.
Acosta started in all three group games for Costa Rica at the World Cup in Russia.
"East Bengal is one of the greatest clubs in India. I convey my best to my new club. My aim is to encourage the other Indian footballers and guide them and at the same time win silverware for East Bengal," Acosta said in a statement.
Acosta has 69 international caps to his name and has scored two goals.
Having made his professional debut for Costa Rican club Santos de Gu?piles in the 2004-05 season, Acosta was with Alajuelense from 2010 to 2016 with whom he won three league titles.
His first appearance for Costa Rica was in March 2011 in an international friendly against Argentina.
East Bengal finished fourth in the I-League last season and lost to Bengaluru FC in the final of the inaugural edition of the Super Cup.
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