An announcement is expected before June 17, when the first full Wales squad will assemble at the Vale of Glamorgan. Gatland's start date has yet to be confirmed but it is expected he would be in position for the 2020 season after taking a six-month break following the World Cup.
The deal will be regarded as a significant coup for the Lions, given that Gatland, 55, has received several approaches since he won the third Grand Slam of his 11-year Wales tenure in March.
It is understood the Lions board agreed for the first time to consider coaches from outside the home unions, conducting its first "worldwide search" for a head coach, but viewed Gatland as "the best of the best".
His insight into the unique challenges of creating a successful Lions environment — Gatland led the tourists to a test series victory in Australia in 2013 and a historic draw against the world champion All Blacks two years ago — were also decisive factors.
The appointment of the head coach two years ahead of the tour will also ensure Gatland, for the first time, will be given a hands-on role in addressing the many logistical, scheduling and preparation challenges.
When he was appointed less than a year before the start of the New Zealand tour in 2017, the schedule, player release and training camps had already been signed off, much to Gatland's frustration.
It is understood Gatland will be given a free hand in selecting his coaching team and backroom staff, while the position of tour manager is expected to go to new Lions chairman Jason Leonard, after a review of the 2017 tour recommended reducing the number of travelling officials.
Gatland and Leonard will aim to ensure that, despite the controversial move to reduce the tour from 10 to eight games and the length of the tour from six to five weeks, the players are given adequate preparation time.
The Telegraph revealed in March the Lions were considering staging a £10 million match at Twickenham or the Stade de France in Paris against a top international side to enable the Rugby Football Union to offer a seven-figure incentive to persuade Premiership Rugby to move its final and give the Lions more preparation time. It is thought Argentina and France are two countries under consideration for the match.
The Lions are due to play their first match in South Africa on July 3, seven days after the Premiership final. The tourists are desperate to ensure there is no repeat of the chaotic start to their 2017 tour of New Zealand, when the squad arrived three days before their first game. Meetings with Premiership Rugby have yet to lead to an agreement.