The body of Tasmanian man Rye Hunt has been identified in Brazil, Foreign Minister Julie Bishop has confirmed.

The 25-year-old man went missing in Rio de Janeiro on May 21.

Ms Bishop confirmed his body was recovered from a beach in Marica, about 25km from Rio, on Thursday. Authorities believe Mr Hunt's body had been in the water.

Ms Bishop said Mr Hunt's family has been informed.

Rye Hunt went missing on May 21. (9NEWS)

Rye Hunt with his girlfriend, Bonnie Cuthbert. (9NEWS)

The family released a statement confirming the body was that of "our Rye".

"It is with deep regret and sadness that clinical testing has confirmed that the body found in Marica, 25km from Rio de Janeiro on 8 June 2016, is that of our beloved Rye Duval Hunt.

"At this stage we await official notification from DFAT, however we can confirm that the body found belongs to our Rye.

"We appreciate your support and sensitivity at this time," the statement read.

Earlier this week, Mr Hunt's family said they were "disgusted" and in disbelief after members of the Brazilian media sent them photos of the body, asking for confirmation of the identity.

Mr Hunt was on a backpacking trip. (9NEWS)

"It goes without saying that this crosses many professional and personal boundaries," the family said in a statement.

"The family ask for privacy and respect at this difficult time."

Mr Hunt went missing after he separated from his travelling companion Mitchell Sheppard, following an argument after the two had taken what is suspected to be a highly potent hallucinogen, known as NBOMe.

He checked into an apartment and was captured on CCTV video leaving a short time later.

Last week, Brazilian authorities called off a 72-hour sea search after a fisherman spotted a body floating off Rio's coast in clothes similar to those worn by Mr Hunt when he vanished.