The semi-submersible rig was detached from its tug during a towing operation when it was hit by severe wind at approximately 4.20am (0320GMT) on Monday, Britain's Maritime and Coastguard Agency (MCA) said in a statement on its website.
There were no people on board the Transocean Winner rig and no risk to life, MCA said. The MCA was monitoring for any pollution.
Scotland police and coast guard rescue workers remained at the scene on the west side of Isle of Lewis, near Carloway.
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