Morgan, 30, opted out of this month's tour because of security concerns, with Jos Buttler leading the one-day team to a 2-1 series win.
England's next white-ball assignments are three ODIs and three Twenty20s against India starting on 15 January.
"Morgan deserves it. His team is continually improving," Farbrace said.
Opening batsman Alex Hales joined Morgan in missing the Bangladesh tour and the decisions were met with surprise in some quarters, while England director of cricket Andrew Strauss was "disappointed".
Former England captain Michael Vaughan described Morgan's decision as a "huge mistake", while Nasser Hussain, another ex-skipper of the national side, said Morgan "should be with his team".
Farbrace said it was great that Buttler had had the experience of leading the side but added: "Morgan will definitely be captain in India. There can't be any way around it."
England's short-format fortunes have risen considerably since the group-stage exit from the 50-over World Cup in 2015.
Earlier this summer they beat Sri Lanka and Pakistan in their ODI series, having also reached the final of the World Twenty20.
The team's attacking style of play - underlined by a record score against Pakistan in August - has also come in for plenty of praise and Farbrace credited Morgan for leading the development.
"He has definitely been the leader and allowed so many guys to play that way," Farbrace said.
Lancashire's Buttler demonstrated his attacking credentials once again with two half-centuries during the three ODIs this month, finishing with 145 runs at an average of 48 with a top score of 63.
However, the 26-year-old wicketkeeper-batsman has not played Test cricket since October 2015 after being dropped because of poor form.
But with England set to play five Tests against the world's top-ranked side India starting in November, Farbrace believes Buttler can win back his place.
"The way he has batted out here, he has looked like he's been batting on different pitches," Farbrace said. "If he can play that way in red-ball cricket, there's no reason he shouldn't be seen as a batter.
"He's on this trip as the second 'keeper to start with, but if he gets an opportunity and plays that way again, there is no reason he can't get back into the side.
"He's shown real maturity with the bat and looked high quality."
Eoin Morgan will "definitely" captain England's short format sides in India despite missing the tour to Bangladesh, assistant coach Paul Farbrace says.