The man, 47, was wading across Cahill's Crossing near Kakadu National Park when he was taken by the 3.3m (11ft) reptile, police said.
Two women made it across the river before realising the man was missing.
His body was found 2km (1.2 miles) downstream on Thursday night, police said. The crocodile was shot and killed.
Local media reported he was from a nearby remote community.
"There is a fair bit of water flowing across at the moment due to the rains and it's a notorious area for crocs there," Northern Territory Police superintendent Bob Harrison told Northern Territory News.
"There are signs up saying don't go in the water but people do. And unfortunately he's paid for that with his life."
The last fatal crocodile attack at the crossing, on the East Alligator River, was in 1987. In that incident, a 40-year-old man died after slipping into the river while fishing with his son.