The match against the Pumas at Cardiff's Millennium Stadium will be the first the Lions have played on home soil since 1986.
Tour captain Brian O'Driscoll has been rested for the game but is set to lead the Lions out for their first game in New Zealand, against Bay of Plenty on June 4 in Rotorua, while Jonny Wilkinson is vice-captain.
Ireland's Gordon D'Arcy will partner Ollie Smith in the centres with Shane Williams and Denis Hickie on the wings and Geordan Murphy at full-back.
Graham Rowntree, Shane Byrne and John Hayes make up the front row with Malcolm O'Kelly and Danny Grewcock the locks.
Woodward said: "Just hearing the names being read out gives me a real sense that the tour is underway.
"I am delighted to be playing this fixture. I have no doubt this will be a very, very stern test for what is an outstanding Lions team.
"There is no doubt we have the makings of a great Lions team. If we get things right off the field we will get it right on the field.
"If we are to go and make history in New Zealand we have to be the best prepared, we have to get the planning exactly right.
"We have to be the best trained and we have to put in the best support teams the Lions have ever had.
"It is my job to make sure that process happens and it has now started."