The swimmer, believed to be a local man, died from "catastrophic injuries after being attacked by what witnesses said was a four-and-a-half metre great white shark at Little Bay on Wednesday.
Human remains were later found in the water.
Police confirmed to AAP they used DNA technology to identify the person who suffered the tragic shark attack - the first since 1963 on Sydney beaches.
Randwick Council has shut a number of beaches including Little Bay, Malabar, Maroubra, Coogee, Clovelly and La Perouse for 24 hours.
"Our entire community is thinking of the family and friends of the victim today," said Randwick Mayor Dylan Parker in a council statement.
"This is a shocking tragedy that our area will feel for a long time."
The council said another assessment will take place on Thursday afternoon to determine if it will reopen on Friday 18 February.
But that did not deter members of the public from having a dip at Clovelly beach, in Sydney's east, in defiance of council's instructions.
Lifeguards are surveying the beaches on jet skis and using drones to check for shark sightings along the coast.
Department of Primary Industries have installed six SMART drumlines between Little Bay and Malabar as part of a shark incident response plan, council said.
SMART drumlines are new technology that allow target sharks to be intercepted beyond the surf break.
Sydney University academic Chris Pepin-Neff, who focuses on policy responses to shark attacks, said "this was not a typical event".
He supported the authorities' decision to close nearby beaches.
"While killing individual sharks does not reduce the risk from shark bites, public education to stay out of the water when sharks are close to shore makes a difference," he said.
A local ocean swim planned for Sunday was cancelled "out of respect for the swimmer and his family".
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