The wicketkeeper-batsman scored 387 runs, including two centuries, and was named man of the series after the final test at Lord's ended in a draw.
"I'm delighted to be back in the limited-overs squads. I feel like I'm striking the ball well," Bairstow told reporters.
"To be back in England and hit the ground running was the main aim. I wanted to back up the form I've shown for Yorkshire," he added.
"I felt like I had a few people to prove wrong. This series and in South Africa I think I've done that."
England coach Trevor Bayliss paid tribute to Bairstow's contribution.
"The form of Jonny Bairstow with the bat has been phenomenal. He's really come of age and looks like he belongs here," the Australian said.
England named uncapped batsman Dawid Malan, fast bowler Tymal Mills and spinner Liam Dawson in the Twenty20 squad with test batsmen Joe Root and Alex Hales rested.
The five-match one-day series against Sri Lanka starts in Nottingham on June 21. The one-off Twenty20 game is in Southampton on July 5.
One-day squad: Eoin Morgan (captain), Jonny Bairstow, Jos Buttler, Steven Finn, Alex Hales, Chris Jordan, Moeen Ali, Liam Plunkett, Adil Rashid, Joe Root, Jason Roy, James Vince, David Willey, Chris Woakes.
T20 squad: Eoin Morgan (captain), Jonny Bairstow, Sam Billings, Jos Buttler, Liam Dawson, Chris Jordan, Dawid Malan, Tymal Mills, Liam Plunkett, Adil Rashid, Jason Roy, James Vince, David Willey.
(Reporting by Ed Osmond; Editing by Tony Jimenez)
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