The ODIs will take place at the Wankhede Stadium in Mumbai on 22, 25 and 28 February.
The Barsapara Cricket Stadium in Guwahati will host the T20 games on 4, 7 and 9 March.
The ODIs form part of the ICC Women's Championship, in which England are currently third.
A victory is worth two points, with the top four teams in the championship table qualifying directly for the 2021 ICC Women's World Cup along with hosts New Zealand.
England will also play a warm-up fixture against a BP XI on 18 February in Mumbai - while the series will be followed by a tour of Sri Lanka, for which dates have not yet been announced.