The 15-man squad has three changes from the side which recently toured South Africa, with pacer Matt Henry and opening batsman Jeet Raval dropping out and Neesham the one addition.
Neesham, who has played nine Tests, has battled a back injury that forced him to return from the series against Australia in November last year. He played for Otago province during the last New Zealand domestic season and recently played for the English county Derbyshire.
"Jimmy has put in a lot of work to make sure he is physically ready for a return to Test cricket," selector Gavin Larsen was quoted as saying by blackcaps.co.nz.
"Having two pace bowling all-rounders in Jimmy and Doug Bracewell helps the balance of the squad, particularly if playing on pitches which demand a spin-heavy bowling attack."
The Kiwis also retained out-of-form opener Martin Guptill, who failed drastically in the two Tests against South Africa last month.
Larsen said India's home record was formidable but the Kiwis were looking for a historic series win.
"We're yet to win a Test series over there and that's motivating for everyone," he said. "We've got three Tests to try create a special piece of history."
New Zealand will play Tests in Kanpur, Kolkata and Indore, followed by a five-match one-day series against India.
Squad: Kane Williamson (captain), Trent Boult, Doug Bracewell, Mark Craig, Martin Guptill, Tom Latham, Jimmy Neesham, Henry Nicholls, Luke Ronchi, Mitchell Santner, Ish Sodhi, Tim Southee, Ross Taylor, Neil Wagner, BJ Watling.
