Wildig is the first of six Town players offered fresh terms at the end of last season to have committed his future to the Shropshire club.
"In the lower leagues of football you're on year-to-year contracts and I didn't particularly think I was going to get a contract so obviously being offered one was pleasing," Wildig told the club's official website.
"I've now signed it so I can go and enjoy the next month of the summer knowing I've got a contract next year.
"I didn't have the best season but I'm a young player and I'm not breaking the bank here to stay."
Shrews boss Graham Turner is still yet to hear back from Jon Taylor, Connor Goldson, Jermaine Grandison, Tom Bradshaw and Ryan Woods regarding their futures.
But in Wildig he has a player who is keen to prove his worth next season having managed just 16 league starts last term following his permanent switch from Cardiff.
"I think the gaffer still sees potential in me," the 21-year-old added.
"I'm good in training and I need to take that into games now. I haven't shown my full potential in games so next year's a big season for me to go and do that, to take what I do in training and reserve games into first team games.
"I need to believe in myself more to go and do that."