Alistair pulled clear of his brother in the final 5km to retain the gold medal he won in London four years ago.
Jonny upgraded the bronze medal he won in London four years ago and held off the attentions of South African Henri Schoeman to win silver.
Yorkshire has now won 11 medals at the Rio Games including four golds.
Alistair joins Ed Clancy and Andrew Triggs Hodge in winning successive Olympic gold medals.
Alistair was a hot favourite to win gold in Copacabana and showed his class in front of waves of supporters, including many from Great Britain.
The Brownlees were at the front of the field throughout the Olympic distance race and moved clear of the field on the 10km run.
The heat of the race was clearly taking its toll with Alistair calling for water supplies within the opening kilometre of the run.
Frenchman Vincent Luis briefly kept pace on the road for home but was soon dropped, leaving the Leeds pair to battle it out.
Alistair stretched his legs after 5km to pull out a half a minute gap over Jonny, allowing him to receive the adulation of the crowd, collect a Union Jack flag and stroll over the line.
Jonny crossed the line six seconds behind and the brothers collapsed to the ground together on the finish line.