Adams, 33, became the first British boxer to win two successive golds since London policeman Harry Mallin won the middleweight division at the 1920 Antwerp and 1924 Paris Games.
"I'm absolutely over the moon," said Adams. "I'm now the most accomplished amateur boxer in Britain that we've ever had... it's been an amazing journey. I've made history."
Ourahmoune's silver was France's fifth medal of the tournament.
Ren Cancan of China, the 2012 silver medallist, and Colombia's Ingrit Valencia Victoria took bronze as losing semi-finalists.
Women's boxing was introduced to the Olympics at the 2012 London Games, with Adams the first of three champions.
Adams had fought the shorter Frenchwoman on four previous occasions, winning every time, but she still needed to use her jab to maximum effect to see off an opponent who won the third round after losing the first two.
"It was always going to be tricky when you've boxed somebody that many times, they know a lot of your movement and you just have to keep changing things up and try to make it different through the bout," said Adams.
Fighting out of the red corner, the Briton was clearly ahead in a brisk first round and used her longer reach to good effect in the second. The third saw Ourahmoune getting in some combinations to narrow the gap but it was all too late.
"You still keep trying, keep hoping that the points add up," said the French fighter. "There's always a little hope but that's sport. Without regrets, I did all I could."
Adams said her second Olympic gold was "well up there" with her first. But the world champion would not be drawn on whether she might be tempted to try for a third in Tokyo in 2020, even if her age would surely be against her.
"I'm going to go on a nice holiday, take some time out and think about what comes next," she said.
(Editing by Clare Fallon)
