Both players are back in the international set-up, having chosen to miss October's Bangladesh tour over security concerns.
Batsman Joe Root is also included after being rested for the 2-1 victory in the ODI series against Bangladesh, but Ben Duckett, Steven Finn and James Vince all miss out.
England have won nine of their last 12 ODIs and head coach Trevor Bayliss said there was no never any doubt Morgan and Hales would return despite deciding not to go to Bangladesh.
"No-one was annoyed that they didn't go," Bayliss told the BBC on Monday. "They are good mates of all the players in the team. There are certainly no problems at all."
Asked if Morgan's position as captain had been weakened by his decision not to tour Bangladesh, Bayliss said: "No, not at all. He's been the captain for the last couple of years during a successful period in white-ball cricket.
"There have been no whispers around the squad or from anyone. In fact, everyone is looking forward to welcoming him back to the fold.".
The selectors on Monday also announced a 15-man IT20 squad for the India series on the ECB website (www.ecb.co.uk).
England will play three ODIs and three T20s on the three-week tour with the first ODI scheduled for Jan. 15 in Pune.
ODI squad
Moeen Ali, Jonathan Bairstow, Jake Ball, Sam Billings, Jos Buttler, Liam Dawson,, Alex Hales, Eoin Morgan (captain), Liam Plunkett, Adil Rashid, Joe Root, Jason Roy, Ben Stokes, David Willey, Chris Woakes
T20 squad
Moeen Ali, Jake Ball, Sam Billings, Jos Buttler, Liam Dawson, Alex Hales, Chris Jordan, Tymal Mills, Eoin Morgan (captain), Liam Plunkett, Adil Rashid, Joe Root, Jason Roy, Ben Stokes, David Willey
(Writing by Ken Ferris; Editing by Frank Pingue)
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