Liverpool Coastguard says three tugs were used to refloat the Ciudad de Cadiz at around 10am this morning.
The ship is now back at the quayside at the Port of Mostyn.
Surveyors from the Maritime and Coastguard Agency will go aboard at 1pm to examine it, to see if there's any damage, and if it's safe to go to sea.
It will then go to Holyhead, where a dive survey will then inspect for any external damage.
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A chance of seeing brighter spells in the south and east this morning but turning cloudier everywhere this afternoon with patchy rain.
Occasional blustery showers overnight and brisk north-westerly winds. Patchy rain will continue during the day tomorrow.