Woodward said: "When we announced the squad a number of players had to prove their fitness before inclusion in the tour party - this included Jonny.
"He has come through it with typical determination and I am delighted that he is able to join the tour party when we assemble on May 17th.
"I have been monitoring his progress over the past few weeks and have been impressed, he has looked good physically and his appetite for the game has clearly not diminished.
"With the likes of (Ronan) O'Gara, (Stephen) Jones and (Charlie) Hodgson, proven world class players, and now Wilkinson we have an incredibly strong group to draw on to face the challenges we will face in New Zealand."
Wilkinson, who embarks on his second Lions tour, added: "To be asked to go on a Lions tour is the ultimate honour. It makes me immensely proud to be going on this tour after a tough season, though also a little nervous in anticipation of what will be an incredible tour."