Anderson has had persistent back problems and missed the Black Caps' recent one-day international series against Australia, Bangladesh and South Africa.
All three players have played for their respective franchises in this year's IPL.
"It's been good to see all three back on the park and bowling; together they add a lot of experience to our squad," New Zealand coach Mike Hesson said in a statement.
"Mitch and Adam have been running in well, and Corey has shown he'll be capable of providing an option with the ball.
"We believe it's an exciting squad; an experienced squad, and one that has the batting power and the bowling variations to prevail in a potentially high-scoring tournament."
New Zealand are in Group A of the Champions Trophy, to be held in England from June 1-18, with Australia, England and Bangladesh the other teams in their group.
Squad:
Kane Williamson (captain), Corey Anderson, Trent Boult, Neil Broom, Colin de Grandhomme, Martin Guptill, Tom Latham, Mitchell McClenaghan, Adam Milne, Jimmy Neesham, Jeetan Patel, Luke Ronchi, Mitchell Santner, Tim Southee, Ross Taylor.
(Reporting by Aditi Prakash in Bengaluru; editing by Sudipto Ganguly)
