Inspector Pears said the shark remained very close to shore for about half an hour after the incident.
The Department of Primary Industries and Regional Development monitored the movement of the shark for some time after the fatal attack.
"It's a tragic incident, very unexpected, a person going out to have a bit of fun in the water," he said.
"It's tragic for the family, friends and people of Broome.
"We live in Broome, it's a close community, a tight community, like other places around the state, particularly remote. We've had a hard year, with some incidents up here. At the same time, this is when communities like Broome shine. We'll pull together ... and try and recover from what is a very sad day."
He said there had been crocodiles and irukandji in the water, but a shark attack was very unexpected. He said the water was very murky and the type of shark responsible for the attack had not been confirmed.
The fatal shark attack has been described by locals as a devastating tragedy that happened very quickly.
The man, a Broome local, was in the water north of the Cable Beach rocks when he was attacked. It is understood he lost his hand and was bitten on his upper thigh.
Beach Hut equipment hire owner Daryl Roberson was at the beach for the last day of his trading season when he heard sirens wailing as multiple police cars sped on to the beach in front of Cable Beach Resort and travelled about two kilometres north to the waters edge.
He said an ambulance followed shortly after but left without any sirens flashing and he later learned it had been a fatal shark attack, with the shark still roaming the waters.
"It was just a devastating thing to have happened," he said. "It was very quick.
"It's a one-of-a-kind [attack], I would think. I remember a pearl diver [more than] 20 years ago got killed and we've had a couple nips here and there from a couple of reef sharks when people have gotten too close but nothing like this."
He said it was most likely a tiger shark as they were common there, attracted when offshore winds pulled lots of tiny bait fish close to shore. He said a hive of fish activity had been witnessed in recent days.
"There's been a lot of fish schools very close to the shore, the bait was everywhere - big schools of mackerel and tuna - and unfortunately where there are big fish, even bigger ones follow."
Francesca Rossi, who was at the beach at the time, said she learnt the "very sad" news from a local ranger after seeing and hearing police cars swarm the area as a helicopter flew overhead.
"A ranger told me what happened and that the beach was closed," she said.
"I heard it was a 55-year-old man, swimming alone and that he'd been bitten on his thigh and lost his hand, but unfortunately died. It's very sad."
Premier Mark McGowan said the attack was a "very sad and traumatic situation" and passed on his condolences to the victim's family.
"It's a traumatic and unexpected event and so I'd just like to pass all of our thoughts on to the people who love the man who has passed away," he said.
"For people who were present, it was a very, very serious set of events. I thank all of those people who attempted to rescue the man in the surf.
"A very sad day for Broome, a very sad day for his family and no doubt there's a lot of grieving people at the moment."
The beach was not patrolled by surf lifesavers at the time as their season ended in early November.
Shire rangers worked with Department of Fisheries to close Broome's beaches. North of the rocks, Cable Beach and Gantheuame Beach are all closed.
Authorities urged people to stay out of the water and not travel to the beaches.
Surf Life Saving WA lifesaving coordinator Nick Pavy said lifeguard services contracted by the Shire of Broome ended at Cable Beach on November 8 and lifesaver services from the Broome SLSC earlier in October.
"SLSWA is very mindful of the effect these types of incidents have on the WA community," he said.
"Particularly those in regional areas where there is a close community network and the area depends on tourism typically linked with the coastline.
"We remind people to choose a patrolled beach where they can and swim between the red and yellow flags under the watchful eye of our lifesavers and lifeguards, to swim with a friend, and always to keep an eye on children around the water."
It has been just six weeks since the last fatal shark attack off the WA coast, after surfer Andrew Sharpe disappeared at a popular surf break at Esperance on the states south coast on October 9.
Authorities believe Mr Sharpe was taken by a shark after widespread reports of a sighting at the Kelp Beds at Wylie Beach in Esperance.
Despite a three-day search, his body was never found. His surfboard and parts of his wetsuit were later recovered.