Cameron Bancroft, who was dropped after two Ashes Tests, has also been called up after his late inclusion to the Australia A side while the uncapped Michael Neser has been included as another seam-bowling option in a squad that covers both a day Test in Brisbane and a day-night Test in Adelaide. It was announced earlier in the day that Will Pucovski had asked not to be considered for selection as he manages his mental health.
"We feel [Joe] was unlucky to miss the Ashes squad," national selector Trevor Hohns said. "Joe's record speaks for itself, he has Test hundreds on the board and has combined very well with David [Warner] in the past. We also like the feel of a right-hand, left-hand combination at the top of the order.
"Travis scored a hundred against a very good New South Wales attack just a few weeks ago and also offers the option of part-time off-spin. Matthew Wade was superb as a specialist batsman through last summer, had a solid Ashes series with two hundreds and strong start to the current domestic season.
"We anticipate Matthew and Travis will give us a strong middle order in support of the top four. Cameron Bancroft is someone who has the ingredients of what we believe makes a good Test cricketer and rounds out our batting group in the squad."
Despite the unconvincing form of a number of the batsman, and the Australia A side falling to 9 for 57, Test captain Tim Paine remained bullish ahead of the series. "I saw that Pakistan are smelling blood in the water or whatever they said," he told reporters in Adelaide. "What happened in Perth has got nothing to do with what is going to happen at the Gabba. The same thing happened in England with the Headingley Test - 'Oh, momentum' and all these words that don't matter. Ball one at the Gabba next week is all square and we start again."
Burns' recall means Marcus Harris, who was the incumbent opener having played the last three Ashes Tests, loses his place while Usman Khawaja has paid the price for a poor start to the domestic season having been dropped in England.
Harris managed just 58 runs in six innings after replacing Bancroft during the Ashes. Though his form has been steady at the start of the domestic season with a century, which came on a featherbed at Junction Oval in Melbourne, and two half-centuries, he has been cut.
Burns failed twice in the Australia A match against Pakistan in Perth but the selectors, Trevor Hohns and Justin Langer, have opted to return to a player who has four centuries in 16 Tests including 180 in his most recent outing against Sri Lanka in February. A stint with Lancashire was cut short by post-viral fatigue syndrome and though he returned for the Australia A tour of England - and scored a century - he was left out of the Ashes squad.
Head, who will also be joint vice-captain with Pat Cummins, was part of Australia A's collapse, but a century in the previous round of Sheffield Shield has been enough for a swift return.
Bancroft has come up on the rails to earn his place after a lean start to the season for Western Australia and not initially being included in the Australia A side until Nic Maddinson withdrew for mental health reasons. However, after Australia A subsided on the second day in Perth, he top-scored with 49 from No. 6 and has the versatility to bat in any position among the top order if required.
Neser, who was part of the Ashes squad, has been rewarded for a strong start to the season and will push for the third pace-bowling slot alongside Mitchell Starc, who has been in outstanding form for New South Wales, and James Pattinson although one of the latter two will be favoured to join Cummins and Josh Hazlewood at the Gabba. However, Neser's impressive performance with the pink ball against Pakistan A in Perth could put him in contention for the day-night Test in Adelaide and he has effectively taken Peter Siddle's position.
"We are blessed to have four of the best fast bowlers in the world challenging each other for spots and most importantly playing as a group," Hohns said. "Cummins, Starc, Hazelwood and Pattinson are daunting pace prospects for any opposition, particularly at home. Michael Neser adds to that group with his ability move the ball both ways, giving the team another bowling option depending on the conditions."
Mitchell Marsh, who took the No. 6 slot at The Oval in September and claimed a maiden five-wicket haul, was not in contention for this squad having broken his hand punching the dressing room wall at the WACA last month.