The 20-year-old forward passed a medical before signing an 18-month contract with Richie Barker's side.
Proctor who joined the Swans from Preston in August, and spent a month on loan at Shrewsbury, is available to face Carlisle United at the weekend.
Proctor said: "I had other options which I had to think about but the manager sold me a very exciting vision of what the club want to achieve and I am delighted to be here.
"Hopefully I can bring a lot of things to the team including goals. It's been a frustrating few months - I just want to be out there playing regularly and hopefully contributing to a successful Crawley team."