The 31-year-old, who made his international debut in 2010, was part of the Black Caps’ past two ICC T20 World Cup campaigns.
Black Caps coach Gary Stead said Milne’s central contract was well-deserved.
“Adam’s worked exceptionally hard and has shown good resilience over the past few years to be in a position to earn this contract offer,” said Stead.
“He’s always been a top-class bowler and we were impressed by his consistent contributions in the recent home summer and tour of Pakistan.”
Finn Allen, Mark Chapman and Blair Tickner have been retained after joining last year’s list mid-season, replacing Boult, Colin de Grandhomme and Martin Guptill – all of whom requested and were granted releases.
Under the terms of the Master Agreement, the players have until June 12 to accept or decline the contract offers.
Players offered central contracts for 2023-24: Finn Allen, Tom Blundell, Michael Bracewell, Mark Chapman, Devon Conway, Lockie Ferguson, Matt Henry, Kyle Jamieson, Tom Latham, Adam Milne, Daryl Mitchell, Henry Nicholls, Glenn Phillips, Mitchell Santner, Ish Sodhi, Tim Southee, Blair Tickner, Neil Wagner, Kane Williamson, Will Young.