Mr Nichols said Cole, an information technology professional from Darwin, either died of chest injuries or drowned as the 650 kilogram (1,430 pound) reptile dragged him under
Moments after the attack, witnesses saw the crocodile swimming upstream with Cole's body still in its jaws, Nichols said.
Police Senior Constable Wade Rodgers, who coordinated the weekend search, said a report on the tragedy would be prepared for a coroner's investigation.
The river is infested with crocodiles, and officials said that as locals the men would have known that.
Crocodile expert Grahame Webb, a Darwin zoologist, said he would not give a swimmer an even chance of crossing the 80-metre-wide river.
"Someone swimming in an area with crocs like that ... crocs are going to zero in on them almost every time," he said. AP