While he is there, the Prince will also undertake two official engagements representing Her Majesty The Queen in Wellington and Auckland at events to commemorate the end of the Second World War.
The invitation to support the Lions came from Sir Clive Woodward, head coach of the touring party, and is for the Prince to spend time with them in the build-up to the second and third Tests against New Zealand, and attend both games.
Woodward said: "I am delighted that Prince William will be spending some time with us.
"It will be a great boost for the team as he is a great supporter of the game. He is going to be with the team for certain periods and it all adds to the sense of occasion around these key Tests."
Prince William, who is currently studying for his final examinations at St Andrew's University, will join the Lions squad for the second and third Test matches in Wellington and Auckland, at the beginning of July.