The 74-year-old, who founded Greece’s largest ferry company Attica, was picked up by the police near the Aspropyrgos industrial zone west of the capital where his kidnappers told the family they had left him.
Greek media said his family had paid a ransom of between £18 million and £13 million.
Panagopoulos, one of the richest men in Greece, did not appear to have been mistreated by his captors but after being held for a week while suffering from a serious illness he was to be admitted to a private clinic in Athens, a police source said.
The police had remained silent throughout the kidnapping drama but media reported that the family of the tycoon had left the ransom as demanded in an isolated spot 60 miles north of Athens.
His wife Katerina had said last week she was “ready to pay the sum” to the abductors, who captured her husband along with his chauffeur in the seaside suburb where he lives.
She appealed to them to release her husband, who needs daily medical treatment including insulin.
The three kidnappers armed with Kalashnikovs used a truck to block the car of Panagopoulos who had just left his home in Kavouri, a residential suburb of the Greek capital.
The chauffeur was found later in a rural area, bound to a tree with handcuffs and with a hood over his head, police said.
Kidnappings are rare in Greece and the perpetrators are usually caught but this is the third high-profile case since the summer.
In December, cardiologist Epameinondas Gerasimopoulos was abducted by two gunmen from his home in the affluent suburb of Vari and is still missing.
In June, leading Thessaloniki industrialist George Mylonas was kidnapped by three men as he drove home with his wife. He was released two weeks later after his family paid 12 million euros according to police.
Two months later, police arrested one of Greece’s most wanted fugitives as the mastermind behind Mylonas’ abduction.