The announcement was made in an IPL media advisory.
Jadhav was ruled out of the entire IPL season due to a hamstring injury after featuring in CSK's opening game against Mumbai Indians, which they won by one wicket.
The team's batting coach Mike Hussey had said on Monday that losing Jadhav, a key player in the middle-order, was a big blow.
Willey, a left-arm medium pacer and a batsman, has featured in 34 One-Day Internationals (ODIs) and 20 T20 Internationals, and plays for Yorkshire in the English County circuit.
Willey will become the 12th Englishman to receive a call-up in this IPL.
CSK's next game is against Kings XI Punjab at Mohali on April 15.