The five members of the Johansen family, one aged only 12, and their two crew – all taken from the Johansen’s 43ft Dynamic yacht ING in the Arabian Sea on February 24 – have been freed by their Somali captors.

Extensive negotiations between the pirates and the Danish government – and a reported payment of $3 million in ransom, according to the BBC – saw the seven Danes flying home on Tuesday. They are said to be in relatively good health.

The family had been on the home leg of a round-the-world sailing trip begun in 2009. They had been trying to get to the Suez Canal in order to reach the Mediterranean, hoping to be back in Denmark by August.

Their Somalian captors had threatened to kill them if a rescue was attempted, as happened to four Americans on their yacht Quest just two days before the Johansens were seized. The Danish yacht was equipped with a computer and they had been blogging, revealing that they were aware of the Quest tragedy at the time of their kidnapping.

The following month soldiers from Somalia’s semi-autonomous Puntland region died in an unsuccessful attempt to rescue the Danes.

Piracy is a growing and very profitable business in Somalia, where political instability has allowed criminal gangs to flourish along the country’s ungovernable Indian Ocean coast. The crews of least 30 vessels, mainly commercial ships, are still being held captive.