Bairstow - who hit 387 runs at an average of 129 and took 19 catches as wicketkeeper during England’s 2-0 Investec series win over the tourists - has been rewarded with a recall to the one-day international squad against the Sri Lankans.
The Yorkshireman, 26, is one of seven members of the Test side named in the 14-man ODI squad - with he and James Vince also in the Twenty20 squad, where there is no place for Stuart Broad.
Bairstow’s Tykes colleague Joe Root is also in the ODI squad, which contains a total of five Yorkshire players with the others being Liam Plunkett, Adil Rashid and David Willey, who are also in the 13-strong T20 squad.
Root has been rested for the T20 game, which takes place at the Ageas Bowl on July 5.
Meanwhile, Cook has paid tribute to Bairstow and has likened his batting to that of three-time Ashes winner Matt Prior.
On Bairstow, named as England’s Test man-of-the-series, Cook said: “It’s a brilliant achievement.
“It’s great to have an attacking batsman coming in and taking it to the opposition.
“He’s very similar to Matt Prior ... when he was at his best, we could often be 100-5 and he’d change the momentum.
“It’s great to see someone who works so hard at his game getting his rewards.”
“Jonny is enjoying both roles. He knows how hard he has to work at his keeping - that is a conversation we do have.
“He knows a couple of chances have gone down, but you don’t become a world-class wicketkeeper overnight.
“He is certainly heading in the right direction.”
England have included uncapped paceman Tymal Mills in the T20 squad along with Middlesex batsman Dawid Malan.
ODI squad: Eoin Morgan (capt), Moeen Ali, Jonny Bairstow, Jos Buttler, Steven Finn, Chris Jordan, Alex Hales, Liam Plunkett, Adil Rashid, Joe Root, Jason Roy, James Vince, David Willey, Chris Woakes
T20 squad: Eoin Morgan (capt), Jonny Bairstow, Sam Billings, Jos Buttler, Liam Dawson, Chris Jordan, Dawid Malan, Tymal Mills, Liam Plunkett, Adil Rashid, Jason Roy, James Vince, David Willey.