Stead announced on Wednesday he would be leaving the job of Test coach at the end of the month, having already relinquished the short format roles in April.
Walter, 49, was most recently coach of South Africa's one-day international and Twenty20 teams but knows New Zealand cricket well after stints in charge of provincial teams as well as his time overseeing a Black Caps "A" tour of India in 2022.
"The Black Caps have been a successful and highly regarded team on the world scene for some time now and it's a real privilege to be given the chance to add to that," Walter said in a New Zealand Cricket statement.
"It's an amazing opportunity to work with such a talented group of players and support staff through a period of time in which so many global events, as well as massive bilateral series, will be contested."
Walter, who led South Africa to the semi-finals of the 2023 World Cup and final of last year's Twenty20 World Cup, is contracted through to the end of the 2028 World Cup, which New Zealand is co-hosting with Australia.
"Rob is a world-class coach with an outstanding pedigree," said NZC chief executive Scott Weenink.
"His success in New Zealand's domestic game, combined with his recent achievements on the global stage with South Africa, makes him the ideal candidate to lead the Black Caps."
New Zealand's next international matches come in July at the start of their tour of Zimbabwe, where they will play two Tests and a Twenty20 tri-series also involving South Africa.
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