Morley will arrive next week, to play a minimum of three games, but only if his commitments with the Sydney Roosters are completed. They are expected to miss the Australian play-offs but could still qualify if they beat Canterbury and both Penrith and Manly slip up.
"Adrian is one of the best forwards in the world and having him on board will be a massive boost," said Chris Caisley.
Bradford are following Warrington and Hull in bringing in a player from the NRL on a short-term contract. Meanwhile, two of the worst-kept secrets in the game have been confirmed with two Bradford players being unveiled as new signings by rival clubs.
Morley's old club, Leeds, have recruited the Bulls' captain, Jamie Peacock, on a four-year deal, after nine years with Bradford.
Leon Pryce is joining St Helens on a three-year contract. "We believe Leon can establish himself as one of the best players in Super League," said Saints coach Daniel Anderson.