While international team-mates Alex Hales, Chris Woakes and Chris Jordan went unsold, Bairstow has been snapped up for 2.2 crore rupees (around £245,000) for next year’s edition.
The Yorkshireman will therefore link up with the likes of controversial Australia opener David Warner and New Zealand captain and county colleague Kane Williamson at Sunrisers, who finished runners-up to Chennai Super Kings this year.
Australia won their first Test match since the ball-tampering controversy as their attack blew apart the India tail for a 146-run victory.
The hosts only needed 15 overs to take the remaining five wickets in Perth and level the series at 1-1.
After starting the fifth day on 112-5, India lost the key wicket of Hanuma Vihari for 28 when he holed out off Mitchell Starc.
From then on, it was just a matter of time before Australia sealed the win.
The win is the first for Tim Paine as captain and Australia’s first in seven Tests, after former captain Steve Smith, vice-captain Warner and Cameron Bancroft were banned for their part in a ball-tempering plot during a Test in Cape Town in March.
The next Test is in Melbourne on Boxing Day.
Kusal Mendis and Angelo Mathews made unbeaten centuries as Sri Lanka repelled the New Zealand attack on a wicketless day four in Wellington.
An impressive 264 not out from Tom Latham and three quick wickets gave New Zealand hope of wrapping up the first Test with time to spare.
However, having started on 20-3 and still needing another 276 to make their hosts bat again, Mendis (116no) and Mathews (117no) guided Sri Lanka to 259-3 at stumps – 37 runs adrift.
Former England captain Alastair Cook looks set to receive a knighthood in the New Year Honours list.
Cook, who is 34 on Christmas Day, will be recognised for his contribution to the sport as he becomes the first England cricketer to be knighted since Ian Botham in 2007.
Cook scored 33 centuries and 12,472 runs in 161 Tests, with each of those statistics standing as England records. He scored a century in his last Test against India at The Oval in September before retiring from the international game.