The 6ft 3in centre-back, 25, has turned down a fresh deal at Adams Park in order to join Shrews, with the move officially going through on July 1.
Winfield started his career with Aldershot before joining Wycombe in 2010 and making over 100 appearances for the club.
Shrews boss Graham Turner told Town's official website: "He's delighted to be joining us and sees it as a big challenge.
"He's a big, strong lad who is effective in both boxes.
"It's a big challenge for him coming here and there's plenty of scope for him to improve yet."
Winfield becomes Town's second signing of the summer after versatile Bolton defender Alex McQuade.