The song, called 'The Power of Four', was specially commissioned by the Lions and will be performed for the first time before Monday's Zurich Test against Argentina in Cardiff.
The Lions, as a composite side from four countries, do not traditionally sing a national anthem before matches and players from previous tours have felt that can give the opposition a psychological advantage.
And, with the All Blacks also engaging in the haka before the Test matches, Woodward felt it was important for the Lions to enjoy their own rallying call.
Woodward said: "I hope players and fans alike will welcome the fact that we have our own song, which can be used to stir the passions and help build the phenomenal camaraderie that is developing between the players of the four countries who have come together as one.
"We are determined to make this the best prepared and the most professional Lions tour ever, and this is one small part of that."
The song was written by composer Neil Myers, and will be performed on Monday by Katherine Jenkins.
It will be made available for fans to download from the internet and the Lions players will have it added to the iPods which they were given last week.
The Lions also hope the song will be adopted by the thousands of Lions supporters making the trip to New Zealand this summer.
"The lyrics are easy to learn, the tune easy to follow and we are confident this will be adopted by the thousands of travelling supporters, and become part of the tour," said a Lions spokesman.
"On previous tours, Lions have said that their opponents can have the psychological advantage of playing their own anthem, whereas a team comprising both the UK and Ireland, it is not possible to play one national anthem for the Lions.
"The players were shown the words on Saturday but they will not be expected to sing it on Monday. The important thing is that everyone is focusing totally on the game against Argentina. But by the time we get to New Zealand, we will all be word perfect.
"As with national anthems there is no obligation on players to sing, but we believe this song will become a popular part of the whole adventure to New Zealand."