Authorities used fingerprints to identify Judson Newton, although they are still waiting for DNA test results, Assistant Police Commissioner Hulan Hanna said late Tuesday.
It is unclear if the 43-year-old Newton was alive when he was eaten.
Newton went on a boating trip with friends off Jaws Beach on New Providence Island on Aug. 29 and encountered engine trouble. Rescuers who responded to a call for help found three men aboard who said that Newton and a friend jumped into the water to try to swim back to shore. Officials launched a search for them, but neither was found.
On Sept. 4, a local investment banker caught the 12-foot (3.6-meter) tiger shark while on a deep-sea fishing trip and he said a left leg popped out of its mouth as they hauled it in.
When officers with the island's defense force cut the shark open, they found the right leg, two severed arms and a severed torso.
One of Newton's friends, Samuel Woodside, 37, told The Associated Press that he was surprised when he heard police say Newton probably drowned.
"To me, he was always a strong swimmer," Woodside said. "I don't know what happened."
Woodside said he and Newton were childhood friends and would go fishing almost every weekend when Newton wasn't working as a sailor on cargo boats or as a chef at local restaurants.
Newton did not favor one fishing spot over another, Woodside said.
"He was a sailor, you see," he said. "Anywhere where he could get a fishing line, he would go there."
Newton was not married and did not have kids, but he left behind his mother and a brother, Woodside said.
The beach near where Newton was last seen is located on the small island where the 1987 shark-terror sequel film "Jaws: The Revenge" was partially filmed. The capital, Nassau, is also on the island.