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McCullum said Pietersen was "shocked" when he first called him about "helping us challenge for a World Cup".
The pair had conversations to reach an agreement and McCullum said Pietersen was "unbelievably enthusiastic" about the prospect.
"The energy he's brought to the group already has been immense and you know I feel very privileged for us to be able to have him as a resource within our dressing room," said McCullum.
"He was obviously a brilliant cricketer. He viewed the game quite differently. He was a winner and he was a guy who left no stone unturned when it came to his preparation.
"A lot of these guys grew up watching Kev play and idolised him.
"As a coach, you're trying to provide these guys with the best environment so that they can try and achieve what they want. Adding Kev is certainly that."
England will hand a debut to Derbyshire opener Aneurin Donald in the first T20, with Phil Salt missing through injury.
Donald, who was born in Wales, has impressed in the T20 Blast and The Hundred with Trent Rockets this year and has the highest strike-rate - 232 - of any batter to have faced at least 50 balls in T20s this year.
Pace bowler Jofra Archer is rested after playing all three Tests against Pakistan, but Josh Tongue is included.
England team to face Sri Lanka in first T20: Aneurin Donald, Jos Buttler, Harry Brook (capt), Tom Banton, Jordan Cox, Will Jacks, Jamie Overton, Liam Dawson, Josh Tongue, Sonny Baker, Adil Rashid.
McCullum's sole responsibility is now for the white-ball side after he was sacked as Test coach following the series defeat by New Zealand in June.
England have appointed fellow New Zealander Stephen Fleming to the role.
The pair must juggle the workloads of England's players as they bid to regain the Ashes from Australia next summer before the World Cup.
"We've already been chatting around how we're going to try and manage some of the workloads of players and make sure we still get our best players available for the big series," said McCullum.
"We'll sit down in the coming days and map out a bit of a pathway for a few guys, but naturally guys can't play all year round.
"You're going to have to work out times that you can take them out of the physical duties of international cricket, freshen up, and then other times that you have them all ready to go.
"They will be easy conversations between two good mates with the motivation of what's right for English cricket."
The end of McCullum's reign as Test coach was tainted by off-field issues in Australia during the Ashes, while captain Ben Stokes and seamer Gus Atkinson missed the second Test against New Zealand in June after an incident in a London nightclub.
Since McCullum's departure seamer Brydon Carse has been involved in a nightclub incident while celebrating a victory for Durham.
Test captain Joe Root said he was "hacked off" and had had a "very strong discussion" in the changing room.
McCullum said he is in "total agreement" with Root and that he wants his white-ball side to be the "fittest, strongest, most dynamic, most robust cricket team in the world".
"There is a lot of talent which sits within English cricket and if people aren't prepared to make those sacrifices and to commit to what you're trying to achieve on the field, then other guys will be given those opportunities," said McCullum.
"It's important for Carsey now to just get his house in order and then work his way back towards banging down the door to play for England, because he's still got a long runway in front of him in terms of his career."
