The 28-year-old heads to the south coast in search of first-team football having been left out of Malky Mackay's 25-man Premier League squad.
Albion boss Oscar Garcia believes the Scotland international is a great addition to his squad.
He told the club's official website: "We were keen to bring extra options, and with Andrea (Orlandi) now ruled out for a longer period than we initially expected, another wide player became a priority.
"Craig is very experienced at this level and knows what it takes to be successful in the Championship. He can play on either wing, or up front as a second striker; he also has international experience and is a player who will improve our squad."