Helen Hudson, south west coastal safety manager for the Maritime and Coastguard Agency, said: "Although everyone is still on board they are in no danger. We are just arranging for another vessel – the Nova Spero – to take the Fryderyk Chopin under tow.
"The captain of the Fryderyk Chopin has indicated he wants to be brought into a UK port so it will probably be Falmouth."
The captain of the 181ft ship sent out an urgent call to the coastguard for help at about 8.30am after high southerly winds tore down the first 120ft (37m) tall mast and he feared the second would follow suit.
At about 11am reports had reached the mainland that the second mast had also fallen.
James Instance, regional coordination centre manager at Falmouth Coastguard, said: "There are currently 47 people aboard the training vessel, no injuries have been incurred and the vessel is awaiting tow. We are constantly monitoring the situation and staying in touch with the Master."
When the alarm was raised, rescue helicopters from RNAS Culdrose, near Helston, west Cornwall were initially scrambled to help the Fryderyk Chopin as part of the rescue mission coordinated by Falmouth Coastguards.
A spokesman for Culdrose said: "We sent one helicopter crew to the scene just in case conditions worsened and things got really nasty and we had to evacuate everyone on board quickly.
"We had a second helicopter on stand-by on the Isles of Scilly just in case the situation took a turn for the worse. By yesterday afternoon both helicopters had been stood down."
The ship has an engine but it is understood the crew was reluctant to use it in case debris and rigging from the two masts got tangled up in the propeller.
Upon receiving the captain's call for help, Falmouth Coastguard immediately put out a broadcast to shipping in the area for assistance.
Three vessels heard the plea and were quickly on their way to help the stricken vessel.
Built in 1992 and named after the 19th century composer, her home port is Szczecin in Poland.
The ship's voyage was part of a Europe-wide project, launched in June this year by the Polish Tourist Organisation to commemorate the 200th birthday of the composer.
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