Update: 11.50am 87 Stena passengers have finally landed at Fishguard in Wales, after 26 hours at sea.
They finally managed to get into their berth at 11am today.
Stena Line's head of PR and Communications Diane Poole says safety comes first and the captain was taking no chances.
Ms Poole said: "Our problem was actually berthing at Fishguard harbour, as it is a very exposed berth. There was absolutely no danger whatsoever to any of the passengers or crew.
"The captain will obviously make decisions and his decisions are based on safety and he will consider the weather conditions and all other elements in relation to taking the vessel safely to the port.
"So he took the ship to a safe destination near Cardigan Bay, so she was able to shelter and stay there all evening."
Update: 10.30am Stena ferry passengers stranded off Wales overnight are finally on their way into port at Fishguard.
The ferry left Rosslare yesterday but could not berth due to high winds and rough seas, and dropped anchor about six kilometres offshore.
Stena Line's head of PR and Communications Diane Poole says the passengers are in good spirits and delighted to be continuing their journey.
Ms Poole said: "They've been watered, they've been fed and they have had a good sleep and last time I spoke to the ship they were having breakfast and heading to Fishguard harbour.
"All-in-all, in relation to what has happened thay are in very good spirits and I think they are all looking forward to getting home or to their work destination or to wherever they are heading."
Earlier: Ferry passengers have spent the night anchored in the Irish Sea after their vessel was unable to dock at Fishguard last night.
Stena Line says the vessel, travelling from Rosslare, could not berth due to high winds and rough seas.
It is currently about six kilometres off the Welsh coast with 87 passengers and 59 crew and will try to land again at midday today.
Met Éireann has issued a status yellow warning for all Irish coastal waters, with strong gales expected on the Irish Sea.
The cold and windy weather looks set to continue throughout the morning but soon clearing to give a bright day.
A spokesperson from Stena Line said "extreme weather conditions" meant they were unable to dock.
"The health and safety of passengers and crew is of paramount importance to Stena Line, therefore the passengers will remain onboard overnight and a second attempt at docking will take place at midday tomorrow (Tuesday)."
Stena Line cancelled last night's planned sailing of the Stena Europe from Rosslare to Fishguard.
Services on the Dublin to Holyhead route are operating with delays.