"Additionally, I'm determined to ensure that Wayne is given the best possible opportunity to succeed in this job when he starts after the World Cup and I will do everything I can to help him".
Pivac will continue as Scarlets boss until the end of the 2018/19 season and will not officially come under WRU employment until July 2019, with Gatland leading Wales into the World Cup.
Over a dozen years, Gatland won the Six Nations Championship in 2008 and 2012 and managed 52 victories in 105 matches with the Wales rugby team.
"I see myself as a Welsh coach", Pivac said.
"I will be doing my best to protect the legacy which Warren Gatland, with the help of those players, will inevitably leave behind".
Welsh Rugby Union (WRU) chairman Gareth Davies and chief executive Martyn Phillips announced the appointment at a scheduled press conference on Monday afternoon.
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Pivac meanwhile led the Scarlets to the Guinness PRO14 title in 2017 for the first time in over a decade, before again taking them to the final this season where they lost to Leinster, along with a European Champions Cup semi-final.
Gatland is a two-time British and Irish Lions head coach, winning one series in Australia and tying with the All Blacks a year ago.
'It's both a huge honour and a privilege to have been asked to be the next Wales coach, ' Pivac said.
"The handover process is something we will plan carefully and commence in detail next summer".
The former New Zealand Police constable has beaten fellow Kiwis Dave Rennie and Scott Robinson to the post, which will be vacated by Gatland after Japan 2019.
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