The appointments, announced by the BCCI secretary Anurag Thakur, meant the only name missing from India's coaching staff from the World Cup was Duncan Fletcher's, whose contract has ended, ESPN Sports Media reported.
Shastri is understood to have been interested in a long-term position, either as head coach or team director but for now, he has agreed for the short-term assignment of one Test and three ODIs in Bangladesh.
Since the BCCI didn't want to rope in new appointees for the short tour, the three specialist coaches were also retained. One of the three is in danger of losing his post after the Bangladesh series.
Meanwhile, the high-profile cricket advisory committee is likely to meet in Kolkata on June 6 to spell out the procedure for appointing the head coach or team director. Besides Shastri, the BCCI is believed to have been in touch with former Sri Lanka coach Tom Moody and Royal Challengers Bangalore head coach Daniel Vettori.
While Moody is understood to have been recommended by VVS Laxman, his colleague at Sunrisers Hyderabad, Vettori has been recommended by Test captain Kohli.
Shastri had been named director of cricket after India's poor performance in the Test series in England last year and the BCCI had appointed Bangar, Arun and Sridhar as assistant coaches at the same time. Their tenures with the Indian team were then extended until the end of the 2015 World Cup.