The move was widely expected and the 33-year-old Benn will now join the squad in Kochi where West Indies play the first One-Day International (ODI) on Wednesday at the Nehru Stadium.
Benn has so far played 25 one-dayers and taken 29 wickets at an average of 31.86 runs per wicket – including three four-wicket hauls.
The six-foot, seven-inch Barbadian last played for West Indies in the recent series against Bangladesh in the Caribbean.
Narine was withdrawn from the tour after he was twice reported by umpires for having a suspected illegal action, while playing for Kolkata Knight Riders during the recent Champions League Twenty20.
He was subsequently banned from bowling in the tournament and the West Indies Cricket Board (WICB) said it had withdrawn the player from the ODI series so his action could be assessed further.