Young will also be in charge of the Barbarians for their annual fixture against England at Twickenham the previous weekend.
Derek Quinnell, the former Wales international and current Barbarians committee member, has been appointed team manager for the two-match tour.
Young, who coached the Barbarians to victories over England and Wales in 2011, said: "I have been privileged to coach the Barbarians on three previous summer tours, but never mind how many times I am invited it is always an honour and one that I cherish.
"It is also a big responsibility to uphold the traditions of the Barbarians and to get the best out of the fantastic group of players they invariably assemble for these matches.
"This will be even more so next summer. The annual game against England is a big enough occasion in itself but to play the Lions on the first match of their own major tour is really a case of the icing on the cake. It promises to be a tremendous tour and all those of us involved will be committed to making it a big success."
The Barbarians have played the Lions once before, at Twickenham in 1977 in honour of the Queen's Silver Jubilee. Quinnell was in the Lions team that day.
Ten years later, Quinnell was on the Wales coaching staff that sent for Young to join their squad for the quarter-final of the inaugural World Cup. Between them, Young and Quinnell have been on six Lions tours.
"I have worked with (Young) before - although it seems a long time ago. He was a young 19-year-old prop at the time but was equal to the task, and two years later he was back in Australia with the Lions and an automatic choice for the Test team that won the series," Quinnell said.
"The other great thing about Dai is that as a player and now an experienced and successful coach, he understands what makes the Barbarians tick and fully respects and furthers the traditions of our club."