Buttler and Mott led England to the 2022 T20 World Cup title in Australia but endured a disappointing 50-over World Cup in India last year, winning only three of their nine matches.
They were then thrashed by eventual champions India in the semi-finals of the T20 World Cup in the Caribbean in June.
England were beaten 2-1 by West Indies in the one-day international series, with defeat in the decider their 12th in 18 ODIs.
Buttler has been out injured for four months but said that absence made him “determined” to lead England’s latest white-ball reset.
“I just want to be present and help develop the next era of white-ball cricket and just really, really enjoy this part of my cricket,” he added.
“When you get an injury like that, it makes you realise how desperately you want to get back.”
McCullum said part of his role is to cheer up Buttler, who he said had been “miserable” at times during England’s recent limited-overs troubles.
“It’s obviously something I need to work on,” said Buttler.
“I’m really excited about him taking over. You can see the effect he’s had on the Test team and the whole narrative around English cricket. He was always someone I’d have loved to play in a team with and now there’s an amazing opportunity to work with him as a coach.”
Buttler will be a specialist batter for the T20 series, with Phil Salt remaining as wicketkeeper, while Marcus Trescothick continues as interim head coach.
Buttler said he made the decision to give up the gloves with McCullum, who did the same during his career to focus on his role as New Zealand captain.
“When he moved to be close to the bowler, he found it incredibly beneficial and a great place to captain from,” said Buttler.
“I’m open to something if it’s going to be good for me, good for the team. I’m quite happy fielding. There are pluses and minuses to both.”
West Indies have announced a 15-man squad for the first two T20s, with seamer Matthew Forde replacing Alzarri Joseph, who is serving a two-match suspension for leaving the field after arguing with Shai Hope during the third ODI.