Farah became the seventh man to win both the 5,000m and 10,000m events at the same Olympics with a blistering last lap that took him over the line in 13 minutes 41.66 seconds.
"I wanted a gold medal for each of my two girls on the way. They could come any day now! It has all worked out well. Two gold medals. Who would have thought that?" said Farah, who was also the first Briton to win either title.
"It's been a long journey of grafting and grafting," he added as spectators chanted his name.
Dejen Gebremeskel of Ethiopia, this year's fastest man, finished in a time of 13:41.98 in silver with Kenya's Thomas Pkemei Longosiwa in bronze.
Reminiscent of the thunderous roars that filled the Olympic stadium a week ago to pull Farah across the line, the 29-year-old timed his race to perfection and delivered a second gold with a courageous last lap he covered in under 53 seconds.
Having been pushed about in the qualifying heats Farah had stayed out of trouble at the back of the pack in a slow set of opening laps and resisted the temptation to kick on when the pace picked up at the halfway stage.
Much like the 10,000, the slow pace was perfect for Farah who was able to move in and out of the pack at will before taking control as the end approached.
With around two laps remaining and showing no signs of the tired legs he had admitted to in qualifying, he made his move to huge roars from the crowd.
Farah picked up the pace and worked hard to see off a number of late challenges before accelerating away from Gebremeskel on the home straight to cross the line to screams and cheers.
An elated Farah began his celebrations by doing a few sit-ups before running to greet the crowd and hugging his coach Alberto Salazar, who has helped turn Farah into a world-class athlete since he moved to America in 2011 to work with him.
Farah's performances will define these Games and will be what many people remember - in 2008 we had Usain Bolt's Lightning pose, in 2012 we had the Mo-bot - and both men, who are managed by the same lucky agent Ricky Simms, did each others' trademark poses after receiving their medals.
"There is no word to describe what I feel right now," he said,
"As an athlete you dream of these moments and becoming the Olympic champion. To do it twice is amazing but to do it twice at your home Games is just impossible to describe.
"You think of the great athletes who have done it in the past and it's so humbling to be mentioned in the same sentence as them.
"Hard work and grafting gets you there. What I've been doing in terms in mileage is incredible but doing that and having a great coach like Alberto Salazar has just paid off for me.
"Usain Bolt is a legend, we won't see his like again and to see him doing my Mo-Bot is just incredible.
"To win three golds at one Olympics and then come back and win three more at another is amazing. If I can come back at another Olympics and do a double then I might be sort of kind of getting there."
Farah was happy with the slow pace of the race and admitted he was feigning just how tired he was after Wednesday's heats.
"I was feeling tired but I was telling people that I felt more tired than I was," he added.
"I knew that if it came down to the last lap then anyone could kick and it worked in my favour so it was awesome.
"On that last lap I wasn’t thinking about staying in the front and letting no-one go past me.
"The crowd was inspiring, it got louder and louder and it reminded me of a football match and when someone scores a goal. I wouldn't have done it if it wasn't for them.
"I didn’t know I had won it until two or three metres from the line."
Farah's next priority is supporting wife Tania as she prepares to give birth to twins, who will now have a medal each. But soon he will look to the marathon - and promoters around the world will be lining up with big cheques to sweeten that deal.
"I still think there is more to achieve on the track, at the Worlds and Europeans," he added.
"I'd like to step up to a marathon one day but not yet because what I'm doing now is working. I will speak to my coach and plan the next few years, but I'll race in Birmingham and then do the half-marathon at the Great North Run, so I'm getting there.
"I'm very excited about the future."
Farah, who moved to England from Mogadishu, Somalia at the age of eight, grabbed headlines in 2010 with 5,000 and 10,000 European titles but his profile has rocketed since moving to the US, winning the world 5,000 title and silver in the 10,000.
This year he added a second European 5,000 title.
Farah's American training partner and friend Galen Rupp, who took 10,000m silver in London, said he was under instructions to protect Farah's small frame.
"I'm thrilled for him, it really couldn't have happened to a better guy," said Rupp who finished the race in seventh.
"He said 'you're a bit of a bigger guy so I'll have you in there to protect me'."
The world's three fastest men this year, Ethiopia's Gebremeskel and Hagos Gebrhiwet, and Kenya's Isiah Kiplangat Koech, were seen as Farah's biggest rivals for gold after setting piercing times this season and having fresher legs.
On the night, Gebremeskel looked the most dangerous of the trio.
His very late charge on the home straight forced Farah to stick the burners on once more having already seen off concerted efforts from American Bernard Lagat and Longosiwa.
"He's a great man. His finishing is really, really good and to be honest mine's not that bad either. On this special occasion he was just better than me," said the 22-year-old Gebremeskel.
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