Somalia’s defence minister said the Somali army and security forces started the rescue of Deborah Calitz and Bruno Pelizzari on Wednesday night.
Ms Calitz and Mr Pelizzari were kidnapped while they were sailing in the Indian Ocean off east Africa in October 2010.
Defence Minister Hussein Arab Isse did not say whether a ransom had been paid.
The pirates had originally demanded $10m (£6m) in return for the release of Ms Calitz and Mr Pelizzari.
The couple’s 20-month captivity is among the longest periods any hostages have been held by Somali pirates.
The couple were working as crew on a yacht on its way from Tanzania to South Africa when they were hijacked.
The ship’s captain, Peter Eldridge, refused to leave with the pirates and was rescued by the European Union’s anti-piracy force.
The freed hostages appeared alongside Mr Isse at a news conference in Somalia’s capital, Mogadishu.
“We are very happy to get our freedom again. We are so happy today and to join our families again,” Ms Calitz said.
A British yachting couple, Paul and Rachel Chandler, were held for more than a year, before being freed in November 2010.
Mr Isse said further rescue raids would take place, referring to a French intelligence agent who was kidnapped in Mogadishu in July 2009.
“We know the whereabouts of the rest of the hostages, including the French agent, and if the kidnappers fail to free them, we will forcefully rescue them,” Mr Isse said.
The European Union Naval Force in Somalia estimates that 213 hostages are currently being held by pirates.
Up to 10 EU naval ships now patrol the waters off the Horn of Africa, which are some of the world’s busiest shipping and humanitarian aid routes.
The anti-piracy force’s mandate, which first started in 2008, was expanded earlier this year and it is now allowed to carry out attacks on the Somali coast against suspected pirates.
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