Shah replaces former Pakistani seamer Aaqib Javed and will be in charge for three months.
Anderson missed the series against Bangladesh due to a shoulder injury.
Kevin Pietersen impressed by Virat Kohli ahead of England's tour of India.
BCCI said it was unable to execute the MoU between the two boards due to financial restrictions levied on it by the Supreme Court.
The first Test match between India and England starts on 9 November at Rajkot.
Batsman may require surgery on a thigh injury sustained on ODI duty against New Zealand.
Hosts reached 171-1 before Moeen Ali and Ben Stokes fought back.
England will travel to India for a five-Test, three ODI and three T20 series.
The Three Lions' spin trio failed to perform in the first Test in Chittagong.
Hosts have two wickets left in hand and require 33 more runs to seal historic victory.
Bangladesh host England in the first Test on 20 October. Find out where to watch live.
Both scored half-centuries during the game in Chittagong.
Pakistan are top of test rankings and India is sport's global powerhouse.
Bangladesh host England in the third ODI on 12 October. The three match series is tied at 1-1.
The three match series is tied at 1-1 with the third ODI scheduled for 12 October at Chittagong.
Bangladesh host England in the second ODI on 9 October. The visitors lead the series 1-0.
Adil Rashid finishes with figures of four for 49 as hosts throw away chances of victory with late collapse.
West Indies will be the visitors to Birmingham in historic match in August 2017.
Stuart Broad is currently regarded as a Test specialist by England's selectors.
Imrul Kayes hits 121 but England win opening tour match by four wickets at Fatullah.
Swann has played 60 Test matches for England.
Leg-spinner Adil Rashid has also clarified his reasons for controversially missing crunch clash at Lord's.