"DNA identification confirmed that the body discovered does indeed belong to the late president," Michalis Katsounotos, a police spokesman, told state radio.
Investigators sealed off a village phone booth south of Nicosia, from which the tip-off originated, to collect fingerprints.
Grave robbers stole Papadopoulos's body on December 11 last year, one day before a memorial service was to be held to mark the first anniversary of the 74-year-old's death from lung cancer.
Police had described the theft as "deliberate and carefully planned," with a marble slab weighing 250kg lifted to dig up the grave.
He was president from 2003 to February 2008 and died in December 2008. It is unclear why his body was stolen.
Papadopoulos made many enemies during his eventful political career.
Cyprus sought the help of Interpol, the Federal Bureau of Investigation (FBI), Scotland Yard, Greece and Israeli police as the police launched an investigation.
Newspapers carried reports suggesting the 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, a member of parliament since 2006, told the AFP news agency 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 Slobodan Milosevic, the late Serbian president.
In 2004, Papadopoulos 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 failedand the Greek sector later joined the European Union.
Northern Cyprus is only recognised by Turkey in the international community.