Bairstow has been picked in place of dropped county team-mate Gary Ballance after making five hundreds for reigning champions Yorkshire in the County Championship where he averages over 100 so far this season.
England have suffered a series of top-order collapses in recent matches and they could not get themselves out of trouble in the second Test at Lord's, where Australia won by a crushing 405 runs to level the series at 1-1.
Bairstow, the son of late former England wicket-keeper David Bairstow, now has a chance to improve on a modest Test average of 26.95 in 14 matches, the last against Australia in Sydney in 2014 when an England defeat meant they suffered a 5-0 Ashes whitewash.
However, he made a match and series-winning 83 not out against New Zealand in a one-day international at Chester-le-Street last month.
"I am very pleased to have been called up," Bairstow, set to bat at number five for England, said Tuesday after being included in a 13-man Test squad.
"Consistency-wise I think I am in my best form and striking the ball well and hopefully this will continue. Playing international cricket is a great challenge but that is why we play the game, he said.

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