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Paul Millachip was swimming at Port Beach near Perth on Saturday (6 November) when he was attacked by the shark.
A large search effort has since been called off, with only a pair of goggles retrieved.
Dad-of-two Millachip, who was reportedly originally from London, was a regular swimmer at the beach.
The 57-year-old was attacked while swimming about 50 metres off the coast, with some witnesses claiming he was attacked by a four-and-a-half-metre (15-foot) great white, while others reported that he was attacked by a great white and a tiger shark at the same time.
Four teenage boys were nearby in a dinghy at the time of the attack and they have been praised for raising the alarm and urging people to get out of the water.
Millachip's wife, who wished not to be named, was also at the beach along with their two kids.
Paying tribute to her husband, she said: "Rest in peace, Paul. He died [doing] what he enjoyed doing the most, which was exercising.
"He was a wonderful man, a wonderful father, and he loved his exercise."
She also thanked everyone who had helped during and after the tragedy.
She said: "A special mention to those young lads in the boat for what they did in what must have been an absolutely terrifying experience for them, so my heart goes out to them and I thank them for what they did.
"I also just wanted to say thank you to all of our friends here in Perth for all the support and love that you've shown us and that's really appreciated because both of our families are overseas and obviously we've been talking to them as well, but it's hard because they may not be able to travel here to be with us."
Praising the emergency services, she continued: "We've been through in quite a lot of detail what they've been doing and how the search has panned out, and they've been extremely thorough and extremely professional and we're really, really grateful for that.
"I wanted to thank also the eyewitnesses, there's a number of eyewitnesses who have given very, very valuable accounts and that's helped piece together what's happened, so we can be very clear that it was actually Paul involved.
"It came out of the blue. But it did happen, you just have to deal with it."
The beach was reopened yesterday with visitors advised to 'remain vigilant'.
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