The popular ground had missed out on hosting big ticket games during 50-over World Cup held in India four years ago.
However, Eden Gardens have organised marquee matches in the past, notably the 1987 Reliance Cup final and 1996 World Cup semi-final, which India forfeited the match to eventual champions Sri Lanka due to a crowd disruption.
BCCI said the chosen venues will have to meet the prescribed requirements.
"These venues will host the matches subject to fulfilling the prescribed requirements of the ICC and BCCI while adhering to the statutory obligations that are mandatory for hosting an International match," said the BCCI in a statement.
The showpiece event of the shortest format will take place for the first time in the cricket-crazy nation. India had won the inaugural World T20 in 2007.
Talking more about the much-awaited tournament, BCCI secretary Anurag Thakur said: "BCCI is extremely proud to host this prestigious event. All the venues identified have hosted many prestigious matches. With this announcement, we have begun our preparations in right earnest. We want this World Twenty20 to be a memorable experience for our participants and fans. I am confident that all the venues nominated will deliver a world class event."
The Board has also constituted a managing committee for the biennial event, of which president Jagmohan Dalmiya will the be chairman and Thakur the convenor.
The other members of the committee are joint secretary Amitabh Choudhary, treasurer Anirudh Chaudhry, vice-president G Ganga Raju, IPL chairman Rajeev Shukla, Chairman, IPL, Ashish Shelar, vice-president of Mumbai Cricket Association and Ashirbad Behera, secretary at Orissa Cricket Association.