"DNA identification confirmed that the body discovered does indeed belong to former Cyprus president Tassos Papadopoulos," police spokesman Michalis Katsounotos told state radio.
The body was found at a cemetery in a Nicosia suburb late on Monday following an anonymous tip-off from a telephone box, he said, without giving further details.
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State television said family members gathered at the cemetery and reporters said the ex-president's daughter, Anastasia, was seen leaving the graveyard in tears on Monday night.
Investigators sealed off the village phone booth south of Nicosia from which the tip-off originated to collect fingerprints.
Grave robbers stole Papadopoulos's body from inside his coffin on December 11 - one day before a memorial service was due to be held to mark the first anniversary of the 74-year-old's death from lung cancer.
Amember of Papadopoulos's personal guard found the grave - less than five kilometres from the discovery site - open when he went to light a candle at the cemetery, as he does every morning.
Police said at the time the robbery was "deliberate and carefully planned," with the perpetrators taking precautions to cover their tracks, but that they knew of no motive for the macabre raid.
Cyprus sought the help of Interpol, the FBI, Scotland Yard, and Greek and Israeli police as it scoured surrounding areas for clues.
Newspapers carried reports suggesting the shocking crime may have been a ransom attempt as Papadopoulos ran a successful law firm before becoming president and his widow Fotini belongs to the wealthy Leventis family.
But Papadopoulos family members said no ransom demand was ever received. "We are completely in the dark and there is very little evidence," the late president's son Nicholas, an MP since 2006, said in January.
He also described as "malicious" theories linking the desecration with an old case involving the law firm of the ex-president and the sanctions-busting transfer of money to Cyprus by late Serbian president Slobodan Milosevic.
Hardliner Papadopoulos was president from 2003 to 2008 and made political enemies during his lifetime.
In 2004, he led Greek Cypriots in rejecting a UN plan to reunify the divided island in a referendum.
Turkish Cypriots backed the plan in a simultaneous vote, but the plan failed and a divided island joined the European Union soon afterwards.
