South Africa-born left-hander Jennings comes in for teenager Hameed, who broke his little finger during England's defeat in the third test in Mohali and will return home to undergo surgery.
The 24-year-old, currently with the England Lions squad in the United Arab Emirates, scored six centuries for county side Durham last season and he will arrive in India on Dec. 5.
Hampshire's left-arm spinner Dawson, capped at Twenty20 and one-day level for England, replaces Ansari, who has been struggling with a back injury.
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England trail the five-test series 2-0.
(Reporting by Martyn Herman; Editing by John O'Brien)
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