Pitt pulled out of the Universal Pictures production last month because he had concerns over the script.
Following rumours that Crowe would step in to take his place, he has taken the role of a journalist whose investigation into the death of a woman leads him to a politician friend.
It is thought that Crowe's signing has avoided a protracted delay in the film's production.
If the film had to be scrapped because of Pitt's decision to pull out there could have been a possible lawsuit, but it is unclear whether Universal will take legal action against the actor.
Crowe will appear alongside Dame Helen Mirren and Ed Norton in the film remake that will be directed by Kevin MacDonald.
John Simm and Bill Nighy starred in the original TV series.