"It is an exciting time to be involved in Australian cricket, with a new captain in Steve Smith and a crop of hugely talented players alongside him with the chance to forge a bright future for our national side," chairman of selectors Rod Marsh said in a statement.
Fekete impressed Marsh in the last domestic season, when he took 37 wickets - more than any other fast bowler - and he also performed well on a recent Australia A tour of India.
"He can generate reverse swing and that ability could be extremely useful in the conditions we expect to encounter in Bangladesh," Marsh said.
West Australian Bancroft, 22, has been earmarked for a lengthy international career.
"Cameron is a player who impressed everyone on the recent A tour of India," Marsh said.
"He can bat for long periods of time ... on that tour he played spin well, fielded brilliantly at bat-pad and his whole demeanour was that of a player who is determined to play Test cricket.
"He's young, hungry and he could become a very good player for us over a long period of time."
Missing from the recent Ashes squad are retirees Michael Clarke, Chris Rogers, Shane Watson, Brad Haddin, Ryan Harris; the injured Warner; quicks Johnson and Hazlewood; and legspinner Fawad Ahmed, overlooked in favour of O'Keefe.
"It's true that Fawad didn't get many opportunities in either the West Indies or on the Ashes tour but when he did get them he didn't bowl as well as I'm sure he would have wanted," Marsh said.
"With Stephen O'Keefe, Nathan Lyon and Glenn Maxwell we believe we have the right number and the right type of spinners for the conditions we expect to encounter."
Australian squad: Steve Smith (capt), Adam Voges (vice-capt), Cameron Bancroft, Joe Burns, Patrick Cummins, Andrew Fekete, Usman Khawaja, Nathan Lyon, Mitchell Marsh, Shaun Marsh, Glenn Maxwell, Peter Nevill, Stephen O'Keefe, Peter Siddle, Mitchell Starc.
- AAP
