The Lions - who fly from Heathrow on Wednesday evening - have won just one Test series against the All Blacks in 10 trips to the toughest of all touring destinations, but Woodward believes his class of 2005 will enhance that tally.
He said: "This tour has been a year in the planning and will be one of the great sporting adventures. We're acutely aware of how big the challenge will be - no-one needs to tell us how tough it is.
"The fact the Lions have won only one Test series in 10 visits says it all. But the message is this - we will be the best prepared tour in the Lions' history and we have the making of a great Test side.
"I've been on a Lions tour as a player so I know it takes time to gel, but we will gel. I know that from what I've seen on the training pitch and the attitude of my players and the coaching staff, we have every reason to feel confident.
"We will go out to win every game and we must reverse that tide of one in 10. It's the Tests that count. If we can win the Test series it will be an achievement to match any other in rugby. We respect New Zealand but don't fear them."
The Lions' 25-25 draw with Argentina at the Millennium Stadium on Monday night was not the best way to start the tour but Woodward insists his 45-strong squad have put the performance behind them.
He said: "Drawing with Argentina wasn't deflating - you have to take it in your stride. You have to start somewhere and now we can get on with it. We were disappointed with the game but no more than that.
"It was a poor performance based on the fact we hadn't played enough times together, no more than that."
Woodward confirmed the Lions suffered no injury setbacks from Monday night.
He said: "No-one is unavailable for the first match on tour. We picked up a few bumps and bruises from Argentina but everyone is fit."