The 32-year-old has dropped down the pecking order at The Hawthorns and has not featured at all this season, but will hope to help the Canaries pull away from the wrong end of the Championship table.
City caretaker boss Jim Duffy said: "I am delighted to sign a player with John's experience.
"The situation we are in demands players who know how to operate in the positions they play.
"John fits the bill, is a strong character and has a proven track record at the very highest level." Hartson has moved to Carrow Road for an initial month, with a view to extending the deal if he impresses and proves his fitness.