The off-spinning all-rounder, who will take over as overseas player from James Pattinson at the end of June, is expected to feature in six of the final seven red ball matches, said the club in a media release.
However, he will miss the trip to Scarborough to face Yorkshire due to international commitments with India, but is expected to return to face Kent, Warwickshire and Surrey in the final three matches of the season.
Ashwin is India's fourth leading wicket taker in Test cricket having claimed 342 scalps at an average of 25.43, including 26 five-wicket hauls. The 32-year-old has also amassed 2,361 runs at an average of 29.14 in his 65 Test matches to date, with a career-best of 124 coming against the West Indies in 2013.
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