In March, a court had sentenced Tsochadzopoulos to eight years in prison for submitting false income declarations. It also ordered the seizure of his home in central Athens and imposed a 520,000-euro ($706,800) fine.
He had spent nearly a year and a half in pre-trial detention, as had his wife, daughter and other close associates.
The corruption case stems from a scandal over a contract for the purchase of German submarines and for Russian anti-aircraft missiles. Tsochadzopoulos had been accused of accepting bribes between 1997-2001 to award the contracts.
Although the bribery charges are beyond the statute of limitations for a former minister, he was convicted of money laundering for using the proceeds of the alleged bribery.
Tsochadzopoulos served as Greece's defense minister from 1996 to 2001 and its development minister between 2001 and 2004. He was a prominent member of the Socialist PASOK party, which dominated Greek politics for much of the past three decades.
The party saw its public support hammered after the financial crisis broke out in late 2009 after PASOK said the former conservative government had fudged the country's financial figures.
Greece then had to get international bailouts to avoid bankruptcy. In exchange for the rescue loans, it had to reduce its budget deficit through punishing spending cuts and tax hikes, which contributed to a sharp fall in output and record-high unemployment.
PASOK is currently the junior partner in the conservative-led coalition government.