Rescue services said a coast guard ship would tow the platform as soon as weather conditions improve.
The oil platform, Bredford Dolphin, operated by Norway's Fred Olson Energy company, recently underwent a regular maintenance procedure, and was being towed to the Gdansk shipyard in Poland.
It went adrift in the south of the North Sea early on Wednesday, after a strong wind and rough seas broke the rope linking it to the tugboat.
The lives of the platform passengers, including British, Norwegian and Portuguese citizens, are not in danger, Solve Tanke Hovden of the rescue services told Norwegian TV.
Helge Haakonen, executive director Fred Olson Energy, said the situation was under control, and weather conditions had already improved, making it likely that the platform will be rescued by the end of the day.
