The 20-year-old has been told he will not be offered a new contract by Cardiff this summer and will pen a deal with Shrews when his current terms expire on June 30.
Wildig spent six months on loan at the Greenhous Meadow this season, making 13 appearances and scoring twice.
Manager Graham Turner told the club's official website: "He proved to us that he's a good footballer. He's very intelligent as a player, he picks out good passes and executes them well."
Wildig is the second player after Asa Hall to join Town as they prepare for life in League One next season, although skipper Ian Sharps, Shane Cansdell-Sherriff and Nicky Wroe have all departed having helped the club to promotion.
