That challenge will be reinforced on Sunday when the squad heads to Rotorua for a traditional Maori welcome - and it then begins in earnest on June 4, when captain Brian O'Driscoll is expected to lead the Lions in their tour opener against Bay of Plenty.
Woodward described it as "the last of the great tours" and said: "I have spent the most part of the last 12 months preparing for this day and it is fantastic to have arrived in New Zealand.
"There has been a lot of travelling but everyone is ready for the fantastic challenge ahead.
"I know what rugby means here, that it is defined in the culture but I think you all know how passionate we are about our rugby.
"I make no apologies for saying I believe this is the best prepared Lions tour in the history of Lions rugby. The squad has the makings of a great Lions Test side.
"I believe this is the biggest sporting event in the world this year and I have done all my planning on that format.
"Why have I put so much effort into this Lions tour? It's very simple. The Lions have been to New Zealand 10 times and lost nine. Not a great record.
"We have a 10% success rate here - that is the size of the challenge we face. To have any chance of winning we have to be at our very very best. Clearly it is an enormous challenge.
"The players here have been successful but if the British & Irish Lions were to win the Test series in New Zealand it would surpass any achievement any of us have achieved in the past.
"We come here with enormous respect for New Zealand rugby, for the New Zealand players and the New Zealand coaching staff - but we have no fear.
"I believe we can win. We have world class players and the challenge in the coming weeks is to blend them into a world class side."