Gatland was the outstanding candidate for the post after leading Wales to the semi-finals of the 2011 Rugby World Cup and last season's Grand Slam triumph. The Lions will tackle Australia in a three-Test series as part of a 10-match tour, which opens with a fixture against the Barbarians in Hong Kong on June 1.
"There is no question it will be one hell of a challenge," Gatland said. "Playing in the southern hemisphere is one of rugby's hardest challenges. The Lions came close in South Africa (in 2009) and our ambition is to win the series in 2013 - and I believe we have the players to do that."
Gatland, 48, will coach Wales in their autumn Tests against New Zealand and Australia but otherwise he will be seconded full-time to the Lions.
Gatland is expected to confirm his full coaching team in October and it would be a surprise if the likes of Graham Rowntree and Shaun Edwards are not involved.
All three were part of the 2009 Lions management in South Africa and received the backing of head coach Ian McGeechan to carry the torch to Australia.
"I am really honoured to have been asked to take the position of head coach," Gatland added. "I really enjoyed the experience as one of the assistant coaches in 2009 and since then have harboured the ambition to lead the tour to Australia next year.
"Over the coming months I will give careful consideration to the make-up of my coaching staff and of course the playing squad itself.
"A Lions tour is unique, it is the ultimate career pinnacle for coaches and players. I want to ensure that we get the tour environment right so that we are hugely competitive and that our fans are proud of the team."
The Lions had initially planned to hold the announcement in April but were forced into a delay after Gatland broke both his heels in a fall at his house in Waikato.