Albion boss Oscar Garcia has moved for Conway after learning that Andrea Orlandi will be out for two months with a knee injury.
The new arrival will be eligible up to and including the Championship game at Middlesbrough on December 14.
Garcia told the club's official website: "We were keen to bring extra options.
"With Andrea 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."