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The postponed fifth Test between England and India will be played at Edgbaston from 1-5 July next year.
The series decider, due to be held at Emirates Old Trafford in September, was called off when India withdrew over Covid-19 concerns.
The rearranged Test will count towards the outcome of the series, which India lead 2-1.
Old Trafford will replace Edgbaston as the venue for the second Test between England and South Africa in August.
England and Wales Cricket Board (ECB) chief executive Tom Harrison said: "We are very pleased that we have reached an agreement with BCCI to creating a fitting end to what has been a brilliant series so far."
The ECB said Old Trafford could not stage the postponed Test because of "complexities in the schedule" and a lack of time to prepare a pitch because of "pre-planned events" at the ground.
India were scheduled to play three Twenty20s and three one-day internationals in England in July.
The T20 series - at the Ageas Bowl, Edgbaston and Trent Bridge - will start six days later than originally planned on 7 July, and the ODI series - at Kia Oval, Lord's and Old Trafford - will get under way on 12 July.
"We would like to apologise again to fans for the disruption and disappointment of September events," Harrison said.
"We recognise that accommodating this extra match means a tighter schedule for the white-ball series. We will continue to manage our players' welfare and workloads through next year."
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