Graham Male, from Romsey, Hampshire, the father of crew member James Male, said: "We are absolutely over the moon.
"We haven't got the full details yet as we are in the process of travelling to the Foreign Office to receive those details.
"From what we have heard it's really what we have been campaigning for."
Mr Male said he wished to thank everyone who had supported the online petition calling for the search to resume.
He said that he was optimistic that they would now find out what has happened to the Cheeki Rafiki and added: "We have to get some kind of resolution now."
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Tuesday afternoon's weather for the west of the region
Tuesday afternoon's weather for the east of the region
Tuesday's weather for the west of the region