The new captains will begin their tenures next month in the limited-overs leg of their South Africa tour, which also features two Tests .Kraigg Brathwaite remains captain of the Test side.
The 39-year-old represented India in four ODIs and as many T20s between 2004 and 2007, picking up five wickets.
Indian vice-captain Smriti Mandhana lost out to Australia's Tahlia McGrath in the women's category.
Nabi stepped down as captain in November, after Afghanistan were eliminated from the T20 World Cup without winning a match.
The move follows their disappointing Twenty20 World Cup exit in Australia.
India are slated to play six white-ball games in New Zealand, including three T20Is and as many ODIs, starting November 18 in Wellington.
The Indian captain added he is fit to lead the side against Jos Buttler's England.
The 23-year-old left-arm seamer delivered for India in the five-run win over Bangladesh in the T20 World Cup here, continuing his impressive run.
Arshdeep Singh and Harshal Patel will fight it out for the specialist third steamer's role.
The 42-run win for Scotland comes exactly a year after they defeated Bangladesh by six runs in their opening first-round match of 2021 T20 World Cup