They are 22-year-old Western Australia batsman Cameron Bancroft and 30-year-old Tasmania fast bowler Andrew Fekete.
The much-changed side will be led by new Test captain Steve Smith, who replaces ex-skipper Michael Clarke.
Batsman Clarke, 34, was one of five players to retire after this summer's 3-2 Ashes defeat by England, while David Warner is injured.
Bowlers Mitchell Johnson and Josh Hazlewood have both been rested after figuring extensively in Test series against West Indies and England.
In addition to Clarke, wicketkeeper Brad Haddin, pace bowler Ryan Harris and batsman Chris Rogers have ended their international careers, while all-rounder Shane Watson has quit Test cricket.
All-rounder Glenn Maxwell, off-spinner Steven O'Keefe and batsmen Joe Burns and Usman Khawaja have been recalled, while leg-break bowler Fawad Ahmed drops out from the squad that toured England.
Australia's first Test against Bangladesh begins on 9 October.
"The retirements of five players from the squad that went on the Ashes tour, as well as issues of injury, form and conditions have brought about a major change in the profile of the touring party from the one that toured the British Isles," said national selector Rodney Marsh.
"But with that change comes a fantastic opportunity for all the players going to Bangladesh."
Left-arm seamer Mitchell Starc is included despite a bone spur in his ankle, which moves around and occasionally causes chronic pain.
"We have got some pretty important cricket coming including the T20 World Cup and we would like to see Starc lead the attack for that," Marsh added.
"But if he can't, he can't. At the moment the plan is for him to keep going."
Australia squad: Steven Smith (capt), Adam Voges (vice-capt), Cameron Bancroft, Joe Burns, James Faulkner*, Andrew Fekete, Usman Khawaja, Nathan Lyon, Mitchell Marsh, Shaun Marsh, Glenn Maxwell, Peter Nevill (wk), Stephen O'Keefe, Peter Siddle, Mitchell Starc.
* Faulkner replaced the injured Pat Cummins on 24 September
Australia have named two uncapped players in their 15-man squad for their two-Test tour of Bangladesh.