The 32-year-old has joined the 2015 ISL champions on a free transfer after the expiry of his contract at South Korean club Suwon FC.
Gavilan played in the second season of the ISL for Atletico de Kolkata. He made 15 starts for the Kolkata franchise, bagging three assists and helped them reach the semifinals, where they lost to eventual champions Chennaiyin FC 4-2 on aggregate.
After leaving ISL, Gavilan has been playing for South Korea's Suwon FC.
Gavilan said he was delighted to return to India and the ISL.
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Chennaiyin FC head coach John Gregory added: "Gavilan has exceptional technical quality with a fantastic CV. He also has the past experience of having played in the ISL two years ago when he had a very good season. He will add great value to our team going forward.
A product of the Valencia youth academy, Gavilan represented Spain at various age group levels. He was part of Spain's U-16 and U-19 Euro success in 2001 and 2004 and was also a member of the 2003 Under-20 World Cup squad that lost to Brazil in the final.
In 2008, Gavilan sealed a permanent move to Getafe and spent six seasons there. In 2014, he moved to Levante but soon joined Greek outfit Platanias.