The New Zealander will be seeking to lead the combined nations to their first back-to-back series success in more than 40 years, having been in charge of the team's last tour -- a 2-1 victory in Australia in 2013.
The Lions' only series victory against New Zealand was in 1971, followed up three years later by a triumph over South Africa.
Gatland, who is again taking a sabbatical from his role as Wales coach, admits it is "the biggest job in world rugby against the best opposition in world rugby."
"Success in 2017 is about going to New Zealand and winning the Test series, and I honestly believe we can do that," the 52-year-old told the Lions' official website
. "If we don't believe that, then we shouldn't even be getting on the plane.
"If there's players out there who have doubts, then make yourselves unavailable because we have to go down there as a squad of players and a group of people who believe 100% that we are good enough to go to New Zealand and win a Test series."
The last Lions team to tour New Zealand, in 2005, lost all three Tests under the guidance of coach Clive Woodward, who had led England to victory at the World Cup two years earlier.
The All Blacks have won back-to-back World Cups since then, defending their title last year in England.
Gatland's Wales team lost in the quarterfinals, as did Scotland and Ireland. England failed to reach the knockout stage, but bounced back under new coach, Australian Eddie Jones, to win this year's Six Nations title.
Wales, Ireland and Scotland filled the next placings above continental rivals France and Italy, giving Gatland encouragement about the depth of players he will have to work with for the 10-match, six-week tour starting next June.
"There is some real talent there at the moment," he said. "There is pace, there's players with footwork. There's experience in the forward pack and there's some size as well; there's some real skill and I am incredibly excited about the potential of a Lions team to go to New Zealand."
Gatland acknowledges the All Blacks -- unbeaten at home since 2009, a run of 42 matches -- have built up an almost mythical reputation since ending the nation's 24-year wait for a second world title in 2011.
His Wales team suffered three Test defeats in New Zealand in June this year, and also lost to provincial side the Chiefs.
"There is something about the mythical thing and the legend, but you push it and find a crack and they can be susceptible to faltering like anyone else," Gatland added. "That's going to be our challenge."