It was Britain's first Olympic Jumping title for 60 years, and came after the Host Nation and the Netherlands finished tied after two rounds.
All four team members - Nick Skelton, Ben Maher, Scott Brash and Peter Charles - then rode again in front of a capacity 23,000 crowd.
Skelton on Big Star, Maher on Tripple X III and Charles on Vindicat all jumped clear to land gold, leaving Netherlands with silver, while Saudi Arabia clinched bronze.
The Dutch cracked under pressure in the jump-off phase, with Mikael van der Vleuten and Marc Houtzager both having fences down.
The last time Britain won an Olympic gold medal was at Helsinki in 1952 and this was the first Jumping medal of any description since a Team silver in Los Angeles 28 years ago.
Skelton said he was more nervous watching his team-mates than riding himself.
'I wish I could have gone four times,' he said. 'They've done great, the lads have done great. Absolutely brilliant.
'I've got a wonderful horse, wonderful owners, it's a dream come true.'
Skelton will now go for a second gold in the Individual event, and he said: 'One's good. Absolutely brilliant. Great for the country, great for our sport. It's taken all these years.'
Absolutely brilliant. Great for the country, great for our sport. It's taken all these years.Nick Skelton