The 32-year-old Smith had always been expected to quit New Zealand after the global showpiece and seek an overseas contract.
He said he has no immediate plans other than to spend more time with his family.
Gatland, who guided the British and Irish Lions to a series draw against the All Blacks previous year, has also been linked with the England job. "I appreciate all the support but, at the end of the day, it's my job to make the right decisions for myself and the team and my family".
"It's been a huge privilege to be part of the All Blacks for such a long time and I'm really looking forward to, and excited by the challenges, of the next 12 months".
"This is a critical process which shouldn't be rushed and shouldn't be made in the turbulent period that tends to follow a Rugby World Cup campaign", he added.
New Zealand Rugby chief executive Steve Tew echoed those sentiments, saying: "Ben has been an incredibly loyal servant of the game and we look forward to enjoying the 2019 season with him".
All Blacks coach Steve Hansen praised the impact of Smith.More news: Phil Jones scores stunning own goal in loss to Valencia
"His record is unsurpassed. We'll get to thank Ben, his wife Katie and his family personally for his contribution to New Zealand Rugby next year, when the All Blacks season resumes, but for now we want to congratulate him on everything he has achieved", Hansen said.
The All Blacks have played 96 test matches under Hansen, winning 85, losing eight and drawing three for an 88.5 winning percentage.
"He is is a great player who will bring a lot to the team".
Crusaders coach Scott Robertson will likely also be in the frame.
He took over the top job in Cardiff in 2002 but had mixed results before returning to New Zealand two years later to again work as Henry's offsider, this time with the All Blacks. With Foster and Wayne Smith, plus specialist coaches, he guided the All Blacks through a gilded era as the world's number one team and to a repeat World Cup title in 2015.
Hansen believes it is necessary to make his intentions clear as early as possible in order to give New Zealand Rugby time to make a thorough search for his successor. Before joining the All Blacks, he coached Wales in 29 Tests from 2002 to 2004, which included taking Wales to the RWC 2003 quarter-finals.