Davies played in two Lions tours in South Africa in 1968 and New Zealand in 1971.
He said: "I'm extraordinarily privileged to be named tour manager. I'm thankful for all the support given to me by the Lions committee and home unions.
"I hope I can fulfil the task put upon me. I'm determined it will be a hugely successful tour.
"Lions tours are unforgettable experiences. This is a great privilege bestowed upon me and I hope I can do a suitable job."
The Lions committee will decide upon the coach for the tour to South Africa after next year's RBS 6 Nations.
Lions chief executive John Feehan revealed that the candidate would not have to be drawn from the current coaches of the four home unions.
Feehan said: "The selection of the coach won't be until after the 6 Nations. We will make the appointment then because it gives candidates the chance to show what they can do between now and then.
"The Lions committee will decide who coaches the tour."
HSBC were unveiled as a principal partner to the Lions tour to South Africa, in a deal that sees them become shirt sponsors.