The 20-year-old has signed a two-year contract at the Liberty Stadium and becomes the sixth signing of Michael Laudrup's time in charge following the acquisitions of Michu, Chico Flores, Jonathan de Guzman, Itay Shechter and Kyle Bartley.
Swansea are awaiting international clearance for the move, and Proctor will initially join the club's Under-21 set-up, and is set to feature in their season-opener on Monday.
He told the club website: "I'm delighted to join Swansea.
"The club has enjoyed a lot of success over the last few years and their style of football has really caught the eye."
He added: "I'm looking forward to being a part of things and trying to impress the new manager enough to force my way into his plans."