All three players missed the Aussies' last Test against England in January due to injury but they will are now fully fit to return to international cricket.
The series against Bangladesh marks Australia's return to red-ball cricket ahead of a busy schedule that includes 20 Tests in 11 months up to the end of next year's Ashes in England.
Australia selector George Bailey said: "They have worked extremely hard, individually and with the SSSM (sports science, sports medicine) teams, over the past few months to return from their respective injuries.
"While this is a 13-player squad, we have players prepared and available should any adjustments be required in the lead up to these matches. As previously stated, the volume of cricket and schedule across the next 12 months are likely to present further opportunities across all formats for many players."
Usman Khawaja's retirement has opened up spot in the middle-order of Australia's Test line-up with Cameron Green likely to move to number 5 with Josh Inglis selected as a spare batter and wicketkeeper in the squad.
Scott Boland will continue to back-up the trio of fast bowlers that includes captain Cummins, Hazlewood and Mitchell Starc with Bailey insisting workload management will be important.
"I think the unknowns are how much workload they have within certain Test matches or within certain series," Bailey said of how the quicks will be managed. "Conditions obviously play a factor at different times as well across the 21 Tests and the various differences we'll face across those as well.
"Our planning is that across the 21 Tests that there will be different times when there will be different names and different line-ups, but not so much forecasting in terms of mapping out that they'll miss certain games. The conditions and I guess the outcomes will dictate that a little bit as well."
The first Test against Bangladesh starts in Darwin on 13 August while second and final game of series begins in Mackay on 22 August.
Australia's Test squad: Pat Cummins (captain), Scott Boland, Alex Carey, Cameron Green, Josh Hazlewood, Travis Head, Josh Inglis, Marnus Labuschagne, Nathan Lyon, Steven Smith, Mitchell Starc, Jake Weatherald, Beau Webster
Darren Lehmann believes Justin Langer would be a strong choice to become England's next Test coach, but insists he has not been approached for the role himself despite speculation following Brendon McCullum's dismissal.
Matt Renshaw admits his international career with Australia "is a bit strange" but was pleased to play a match-winning innings in the series-clinching T20I victory against Bangladesh in Chattogram on Friday.
Matt Renshaw struck a career-best 89 not out from 52 balls to help Australia beat Bangladesh by seven runs in the second T20I as the visitors took an unassailable 2-0 lead in the three-match series.
Joel Davies starred with the ball on international debut to help Australia beat Bangladesh by four wickets in the first of three T20Is in Chattogram on Wednesday.
