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Bayliss will replace Anil Kumble after the former India cricketer's contract was not renewed following a poor string of performances by the side under his guidance.
Bayliss will step down from his current role with the England team after the Ashes beginning next month.
It remains to be seen whether the BCCI will stick with Shastri or go for a new head coach.
Bayliss, who has been in charge of England since 2015 and led them to the top of the ODI rankings last year, has a contract until September.
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