The 32-year-old Scot has penned a one-year deal after completing a successful trial period with Gareth Ainsworth's side.
Craig scored 13 goals in 28 appearances for Partick last season on their way to the Scottish First Division title.
"I'm delighted to be here," he told the club's official website. "It's a change of scenery for me moving south of the border and it's a challenge I'm relishing."
- Sports & Recreation
- Gareth Ainsworth
- Scottish First Division