The Scotland international has impressed during his stay at the Amex Stadium, but his deal expired after the weekend's win over Middlesbrough.
Brighton assistant boss Nathan Jones told The Argus: "We have got five that can play wide, including Craig, and he offers something different.
"On the pitch he has been what we knew but off the pitch he has been phenomenal. He fitted in so quickly.
"That was a conscious effort. His wife was pregnant but he moved his family straight down. The loan market is very important and you have to be thorough.
"There have been some we've enquired about who haven't quite fancied it, so we put them to one side.
"We don't want them, we want the ones who are desperate to play for us. He was one I had earmarked before I even came here and he has done brilliantly."