The Brit becomes just the second athlete to complete the track double across both distances in successive Summer Games after he won gold at both events four years ago in London.
His victory also saw Great Britain's medal tally beat the haul from London 2012, with the nation's 27th gold taking the overall total to 66.
Finland's Lasse Viren achieved Farah's feat at the Montreal 1976 Olympics, but Farah's latest double is unparalleled given his success at the World Championships in the intervening years.
Indeed, the 33-year-old won both the 5,000m and 10,000m in Moscow and Beijing to become the first man to do so at three straight global meets, while Saturday's success saw him break fresh ground on the track.
Farah stumbled in the final lap of his 5,000m heat on Wednesday but overcame the scare to book his place in the showpiece race, qualifying in third.
But there was little sign Farah was willing to cross the line behind his competitors on this ocassion as he stormed to his became the first British track and field athlete to win four Olympic gold medals.
He said on BBC One: "I can't believe it. My legs were a bit tired after the 10k. I don't now how I recovered. People were bringing me food in my hotel room, but it is every athlete's dream.
"(It show) I didn't just fluke it in London, to do it again is incredible. I just want to see my kids and hang this medal around their necks.
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"I was surprised by the first lap, I thought it was going to be a slow race. They had a plan, they wanted to take the sting out of me, but when I hit the front, I wasn't letting anyone past me.
"It has been a long journey, but if you dream of something, have ambitions and are willing to work hard then you can get your dreams."
