Gatland led the Lions to a series victory over Australia in 2013 and a drawn series against New Zealand in 2017. He was also an assistant in 2009 when Ian McGeechan's Lions lost 2-1 in South Africa.
Gatland, who led Wales to the Six Nations title this year, will stand down as the country's coach after the Rugby World Cup in Japan, having won three Grand Slams during his spell as the longest-serving coach in their history, having taken over in 2007.
Previously he has taken a sabbatical from his Wales duties to dedicate himself to the Lions but now he would be free from any distractions from when the World Cup ends on Nov. 2.
Gatland said after the last Lions tour that he was frustrated by limited time given to prepare the team and by the shortened nature of the tour. He was also not happy at his treatment by some areas of the New Zealand media.
At the end of that tour he told journalists: "I'm done, I hated the tour. What I've learned from my Lions experiences is how difficult it is to put some continuity together in terms of people and staff, and the lack of preparation time. Let someone else do it. Let someone else reinvent the wheel."
Gatland, 55, has mellowed but will have to deal with an even tighter schedule in 2021. No official dates have yet been released but the tour is expected to last five weeks, featuring eight matches, down from six weeks and 10 games in 2017.
It is also likely to run from July into August - by far the latest in the year of any Lions tour - following the changes to the international calendar that take the European domestic seasons through to late June and give him only three weeks with the players before the first tour game.
The Lions' last series victory against the Springboks came in 1997, also under McGeechan, when the host nation were world champions.
(Reporting by Mitch Phillips, editing by Christian Radnedge)
