Lars Borg, a spokesman for the Copenhagen police, said it was unclear how or why the man had entered the pit, but said investigators could not exclude suicide as a motive. The victim is a foreign national who holds a Danish residence permit, but police would not immediately release his identity or his nationality.
"Everything indicates that the tigers have killed him," Mr Borg said, noting an examination of the body showed the man had been bitten on the thigh, chest, face and throat.
His body was found surrounded by the park's three Siberian tigers by a zookeeper early on Wednesday morning.
Mr Borg said the man appeared to have entered the tiger area from a low wall surrounding the den and then ending up in the moat inside the enclosure. "He has been in the water and the animals must have seen that and attacked him," Mr Borg said.
Investigators were going through CCTV-camera footage to try to establish the man's path inside the park.
Copenhagen Zoo manager Steffen Straede said it was the first time in the zoo's 152-year history that such an incident had occurred, and there were no plans to reassess its security or to put the tigers down.
"If a person really wants to get in (there), we cannot prevent it from happening," he said.