Fifteen members of the team had been abducted last May in Anbar province, an al-Qaeda stronghold west of Baghdad, on their way to a training camp in Jordan.
The bodies were found in western Iraq, near the town of Ramadi. Two of the team are still missing.
In the past two years many Iraqi sports officials have been seized in sectarian attacks or held for ransom.
Olympic hopes
Members of the Sunni Anbar Salvation Council, a group fighting al-Qaeda in the province, found the remains of the 13 taekwondo team members, Iraqi police said.
"We were hoping that we would see them alive and competing for their country in international championships"
The remains - including bones, skulls and shreds of uniforms - were taken to Imam Ali Hospital in the Shia neighbourhood of Sadr City, Baghdad.
DNA tests will be used to identify the athletes, a hospital official told Associated Press news agency.
The athletes were members of a club that aimed to send competitors to the Olympics, Hussein al-Obeidi, secretary-general of Iraq's National Olympic Committee, told AP.
"We were hoping that we would see them alive and competing for their country in international championships," Mr Obeidi said.
Hundreds of mourners gathered in Sadr City on Saturday at a funeral procession for the athletes, who will be buried in the Shia holy city of Najaf.
Last year, an Iraqi international football referee, a member of the Iraqi Olympic football team and a national volleyball player were abducted.
Iraq's national wrestling coach was killed in Baghdad, while 30 other Iraqi sports officials, including the chairman of Iraq's Olympic Committee, were also seized from a sports conference in Baghdad.
Some were victims of sectarian attacks or held for ransom, others were targeted by radical Islamists who disapproved of their activities.
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