Nasir Hossain and Shafiul Islam return to the 14-man squad for the first Test against Australia in Mirpur.
Starc out; Faulkner, Christian in for India tour in September and October, Tim Paine name for T20.
In-principle agreement signed after final round of face-to-face negotiations in Melbourne on Thursday.
They host West Indies, Pakistan, England and Australia in next summer.
India to play 23 International matches from September to December 2017 against New Zealand, Australia and Sri Lanka.
Two-Test tour in August confirmed but Starc and Marsh brothers rested from 13-man squad.