The Kulluk (CULL'-uck) was lifted off rocks at 10:10 p.m. Sunday.
It reached its anchoring point about 12 hours later in Kiliuda (kih-LOO'-dah) Bay, where it's out of the worst of waves and wind offered by the Gulf of Alaska.
Shell incident commander Sean Churchfield says the vessel came off the grounding relatively easy under tow by the 360-foot anchor handler Aiviq (EYE'-vick).
Salvors reported swells of 15 feet, which diminished after the vessels reached protected waters.
The trip covered about 45 nautical miles at about 4 mph.
The Kulluk was attached to a second vessel, a tugboat, after it reached the bay.