The series begins with the first of five T20s on Wednesday in Kolkata (13:30 GMT) before three one-day internationals.
The ODIs act as England’s preparation for the Champions Trophy in Pakistan and Dubai which starts on 19 February.
England have lost their last three 50-over series while Buttler averages 27.00 in the format since March 2023.
He did not play an ODI last year because of injury and has only one score over 50 in his past 15 innings in the format.
“He is smiling. That is good. He is very happy at the moment,” said McCullum, who replaces Matthew Mott after the Australian’s dismissal following the T20 World Cup in June.
“He’s had a pretty good career already. His best years could definitely be ahead of him.”
England’s recent white-ball struggles have come as the Test side has taken precedence in the build-up to this winter’s Ashes series.
Buttler has often been without key players for series but in India he has a near full-strength squad, including quick bowlers Mark Wood and Jofra Archer.
Joe Root was left out of the T20 squad but is in line to feature in the ODIs, having last played in the format at the 2023 World Cup.
McCullum, who has instilled an aggressive, attacking approach into the Test side, said he wants his white-ball side to play “watchable” cricket.
“With the talent we have there is no reason why we can’t,” he said.
“We have a batting line-up as powerful as any in the world, gun spinners, very good fielders and guys who bowl absolute rockets with the ball.
“We have got options there to be able to entertain and give ourselves the greatest chance of success.”