Both teams met on Thursday to discuss how they would recognise the anti-racism movement after the West Indies knelt to show their support before their matches in England this year.
"We agreed we will support West Indies and will take a knee after the umpires call play," Southee said.
"It's something that is very important to the West Indies and something we will support over their tour while they're here."
West Indies Twenty20 captain Kieron Pollard said their team were pleased to have the support of the New Zealand side.
"It's something we feel very strongly about," Pollard said. "It's something we want to inculcate around the world because it has impacted a lot of lives all around the world.
"It's something we will continue to do to make gestures that is positively geared towards that. We have come together with the Black Caps and we thank them for their support.
"It means a lot to us as individuals and hopefully over time everyone will understand how serious this matter is."
West Indies test captain Jason Holder and the team were given an award for their efforts to spread the anti-racism message that was amplified by the death of George Floyd in the United States this year.
While England knelt during the West Indies series, they did not repeat the gesture during games against Pakistan and Australia, prompting some criticism.
