Ricky Ponting will lead the one-day world champions who will start overwhelming favourites to win their three-match limited-overs series.
"We were always going to name our strongest sides. There was never any doubt about that," Australia's chairman of selectors Trevor Hohns said in a statement.
"The players want to play in this series and they thoroughly deserve that opportunity."
Waugh, 38, said earlier this month he had no intention of retiring yet. Bangladesh is the only Test-status nation he has not played against.
Batsman Damien Martyn was left out of the Test side while he recovered from a broken finger but was included in the one-day side, pending a fitness test.
"Damien Martyn hasn't been chosen for the Test match because his injured finger just isn't quite right," Hohns said.
"The medical staff are concerned with his lack of preparation and at this stage we're committed to making sure Damien gets himself 100 per cent right."
Australia are due to play Bangladesh in two Tests in Darwin and Cairns and three one-dayers.
Test squad: Steve Waugh (captain), Ricky Ponting, Andrew Bichel, Adam Gilchrist, Jason Gillespie, Matthew Hayden, Brad Hogg, Justin Langer, Brett Lee, Darren Lehmann, Martin Love, Stuart MacGill, Glenn McGrath
Limited-overs squad: Ricky Ponting (captain), Adam Gilchrist, Michael Bevan, Andrew Bichel, Jason Gillespie, Ian Harvey, Matthew Hayden, Brad Hogg, Brett Lee, Darren Lehmann, Damien Martyn (subject to fitness), Glenn McGrath, Andrew Symonds.
