Williamson, who led New Zealand to victory in the inaugural World Test Championship final against India at the Ageas Bowl in 2021, will continue as white-ball captain.
"Captaining the BLACKCAPS in Test cricket has been an incredibly special honour," he said. "For me, Test cricket is the pinnacle of the game and I've enjoyed the challenges of leading the side in the format.
"Captaincy comes with an increased workload on and off the field and at this stage of my career I feel the time is right for this decision.
"After discussions with NZC, we felt that continuing to captain the white-ball formats was preferable with two World Cups in the next two years.
"I'm excited to support Tim as captain and Tom [Latham] as vice-captain. Having played with both of them for most of my career, I'm confident they'll do a great job.
"Playing for the BLACKCAPS and contributing in all three formats is my number one priority and I'm looking forward to the cricket we have ahead."
Southee, who has previously captained in 22 T20Is, said: "It's been a surreal few days and it's just a massive honour to be appointed as Test captain.
"I love Test cricket, it's the ultimate challenge and I'm really excited by the opportunity to lead the team in this format. Kane's been an outstanding Test captain and I'm looking forward to working with [coach] Gary [Stead] on how we can build on that."
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