The spear fisherman, named in local media as John Craig, was underwater off Western Australia state Friday when his boat was swept away due to engine problems and strong currents.
"I put my head in the water to check I was in the same place and suddenly saw a huge four-metre (13-foot) tiger shark approaching within arm's reach," Craig told commercial broadcaster Channel Nine.
"It was easily the biggest tiger shark I've been in the water with and that's saying something having worked as a dive instructor for over 10 years."
Craig said a sandbar whaler was also closing in on him in the shark-infested waters near Shark Bay as he made the decision to swim back to shore.
"I have to admit that at this point I thought I was gone, four nautical miles out to sea with a huge tiger shark following me. I thought this was it, this is how I'm going to die," he said.
"The shark would disappear into the gloom then suddenly reappear behind me, just keeping pace with me behind my fins."
Craig kept his speargun pointed behind him as he embarked on a swim of "pure endurance", eventually losing the shark.
"It's an absolutely incredible story," Shark Bay Volunteer Marine Rescue commander Greg Ridgley told Perth's Sunday Times.
"He swam at least five miles in shark-infested waters, I just can't believe anybody could do that. It's such a massive effort, in that short timeframe too."
There have been 14 encounters off the nation's vast coastline this year, including the death of a 17-year-old girl mauled by a shark in full view of her parents in Western Australia.
Experts say incidents are increasing as water sports become more popular and baitfish move closer to shore, but fatalities remain rare.
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