Nash, 27, was a member of Britain's men's coxless four that won gold in Rio, securing Britain's fifth consecutive Olympic title in the event.
The three-time world champion claimed Olympic bronze four years ago alongside Will Satch in the men's pair.
"I'd like to thank everyone that supported me," said Nash. "I'm going to take a different tack professionally."
He said he would miss working with the "most dedicated, driven and dogged athletes, coaches and support staff in the world".
He added: "I'll miss exploring the limits of fatigue and laughing about it with the lads. I'll miss lining up next to the best rowers in the world and sharing that infectious, nervous energy on the start line.
"And of course I'll miss all those times I got to cross the finish line first."
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Olympic gold medallist George Nash has announced his retirement from rowing to take up a role as an engineer.