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.
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.
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"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.
But Yorkshire coach Jason Gillespie, a former Australia fast bowler, said Bairstow was now a much-improved batsman.
"It is important that those people who don't watch much county cricket don't pipe up with opinions based on his past experience in Test cricket because we're talking about a different beast right now," Gillespie wrote in his Guardian column.
The 25-year-old scored three hundreds and two fifties in his first 10 innings for England but has found scores harder to come by of late.
"He has scored a heck of a lot of runs over a short period of time," Bairstow, also 25, said of Ballance.
"But it is just one of those disappointing things and, hopefully, I will be able to get in and score runs. I have been very positive at the crease this season and will try and take that into the Ashes series.