Willey, an England international, is a left-arm medium pacer and a batsman, who has featured in 34 One-Day Internationals (ODIs) and 20 T20 Internationals.
Willey will give CSK an attacking option with both the bat and ball. He can bowl at the death and is also a useful hitter of the ball.
He has opened the innings for Perth Scorches in the Big Bash League but bats at No.7 for England.
The Mahendra Singh Dhoni-led side's next game in the IPL 2018 is against Kings XI Punjab at Mohali on Sunday.
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