Bancroft gets his chance after scoring heavily in this season's domestic Sheffield Shield competition, and replaces Matthew Renshaw as David Warner's opening batting partner.
Paine is the selection bolter and gets the nod over Matthew Wade and Peter Nevill, despite few appearances for his Tasmania state side behind Wade this season.
National selector Trevor Hohns said Bancroft earned his call-up to the Test side for the first two in Brisbane next week and in Adelaide in early December.
"He is a very talented and tough cricketer who shows a good temperament for Test cricket.
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"He has thoroughly earned and deserves his call-up following some outstanding performances in the early rounds of the Sheffield Shield competition this season."
Paine is a shock selection and has been named for his first Test in seven years, having last played for Australian in October 2010.
"Tim was identified as an international player a long time ago and has always been renowned as a very good gloveman, also performing well for us whenever he has represented Australia in any format," Hohns said.
Shaun Marsh, 34, also returns again to the Australian squad and will bat at number six.
"Shaun is playing very well at the moment, having scored consistently in the One-Day Cup and first three rounds of the Sheffield Shield competition," Hohns said.
"He is a versatile player who can slot in anywhere in the batting order and will add valuable experience to the batting line-up."
Paceman Chadd Sayers has been added to the strong fast- bowling line-up in the squad along with Mitchell Starc, Josh Hazlewood, Pat Cummins and Jackson Bird to give selectors options depending of the state of the Gabba pitch for next week's first Test.
"He swings the ball with good control and knows the conditions well at his home ground. He gives us this bowling option if required."
Renshaw and Wade were omitted from the Test squad with Hohns saying Wade was left out because of "inconsistent performances with the gloves and lack of form with the bat".
Hohns said the selection panel did not feel Renshaw was batting well enough at this stage to earn Test selection.
"We still view Matthew as a player of immense talent, but he is out of form at the moment and we don't feel an Ashes Test match is the best place for him to find form," he said.
Australia - Steve Smith (capt), David Warner, Cameron Bancroft, Jackson Bird, Pat Cummins, Peter Handscomb, Josh Hazlewood, Usman Khawaja, Nathan Lyon, Shaun Marsh, Tim Paine, Chadd Sayers, Mitchell Starc.