The 23-year-old hit the wall first in 7min 38.19sec, the fifth-fastest time ever, to be crowned 800m freestyle champion in La Defense Arena.
The only other gold won by Ireland in an Olympic pool came at Atlanta in 1996 when Michelle Smith collected three.
Wiffen, the first Irish male swimmer to win a medal of any colour, couldn't hide his emotions when the national anthem played as he stood on top of the podium.
"I don't normally cry, so I really hope that nobody's gonna see that," he said.
"But, yeah, it did come out of me, and it's obviously just a special moment.
"I've never heard that national anthem at an Olympics before, and it's just crazy to say that it was me standing on a number one podium here for the first time."
Wiffen, who also won the 800m at the world championships in Doha this year, came home ahead of American defending Olympic champion Bobby Finke (7:38.75) and Tokyo silver medallist Gregorio Paltrinieri (7:39.38) of Italy.
He took control at 400m after Australia's Elijah Winnington went out hard but tired and was reeled in.
Paltrinieri made at a move at 600m and led to the final turn before Wiffen came roaring back to rewrite the history books.
"To be fair, normally I do only train one way and that's just to try hold on, burn everybody out in the middle," he said.
"But I knew I Olympics is completely different. You don't know how you're going to feel in the first 100.
"So really, my first part of the race was absolutely terrible. My stroke was all over the place, I was just so nervous.
"But luckily I had a good enough speed to keep it going and I was still in the race. Then my goal was to keep building."
Wiffen paid tribute to his identical twin brother Nathan, also a distance swimmer who missed out on qualification for Paris, for urging him on.
"I tell you what, the only voice I heard in the crowd was my twin brother Nathan's," he said.
"I've dreamed of this every day of my life.
"I know that I seem very confident on the outside, but there's always that little tiny feeling that, you know, can I do this?"
