The 20-year-old midfielder spent six months on loan at the Greenhous Meadow this season, helping the club clinch automatic promotion to League One.
And when he was told by parent club Cardiff that there would not be a new deal on the table this summer, Shrews boss Graham Turner had to do little to convince him that Shropshire was the right place to come.
"I'm delighted," Wildig told the club's official website. "As soon as I knew the manager was interested in keeping me, my mind was made up.
"Even when I had a difficult time last season and I was out of the side after being injured, everyone at the club was still good to me. It was great to get back in the team towards the end of the season and it was exciting playing for a side at the top of the league and going for promotion."
Wildig is Town's second summer signing after Asa Hall, although captain Ian Sharps, fellow defender Shane Cansdell-Sherriff and midfielder Nicky Wroe have been lured elsewhere. Wildig added: "I know we've lost a few players from last season, that's football, but there's a lot of good players at the club and new signings will come in."
