The 62-year-old former Wallabies coach beat out Jamie Joseph for one of the biggest jobs in world rugby after an extensive recruitment process that started when Robertson stepped down in mid January.
Rennie, the first All Blacks coach with Pasifika heritage, was handed a contract through to the end of next year's World Cup but will honour his commitment to Japan's Kobe Steelers before preparing New Zealand for the July tests.
"Coaching the All Blacks is an incredible honour," Rennie said in a New Zealand Rugby statement.
"I'm extremely proud to have been entrusted with this role and understand the expectations that come with it."
Robertson stepped down in the wake of a critical review of his stewardship of the team last season, when the All Blacks won 10 of 13 tests but were humbled at home by the Springboks and also lost to Argentina and England.
New Zealand Rugby chairman David Kirk made it clear that there were high expectations about the type of rugby the All Blacks would play.
"He is a world-class coach who has consistently shown he can build strong performance environments and win," the former All Blacks skipper said.
"Dave understands what it means to coach the All Blacks and play a style of rugby that reflects who we are as New Zealanders.
"Dave has a clear direction for the team that gives us confidence the team will be well positioned to perform as we head into the 2027 Rugby World Cup."
Rennie, who has Cook Islands heritage through his mother, made his name as the coach of the New Zealand under-20 team which won three junior world titles between 2008 and 2010.
He enjoyed more success in Super Rugby as coach of the Waikato Chiefs side which clinched back-to-back titles in 2012 and 2013 before moving to Scotland with the Glasgow Warriors.
He was appointed Australia coach in late 2019 and oversaw 34 tests over three seasons - winning 13, drawing four and losing 18 - before being sacked in early 2023 to make way for the ill-fated return of Eddie Jones.
"I'm really clear on the way I want the All Blacks to play and I look forward to working with the players, management team, and the rugby community," Rennie added.
"We have a lot of talent here and we will be working extremely hard to make the country proud."