The double world champion earned an average score of 15.691 to become only the second man from communist North Korea to win an Olympic gold medal in gymnastics, following the success of Pae Gil-Su on the pommel horse at the 1992 Barcelona Games.
"This gold medal is a joy for my country and I think it will bring a sense of victory and courage to the people of my country," said Ri, who described it as the greatest moment of his career.
At the victory ceremony, he saluted with his hand to his right temple throughout the national anthem as the flag of North Korea was hoisted.
"I was filled with a lot of emotions and joy because I thought I was able to bring a sense of victory and glory to our leader," he told reporters, cradling his medal in his hand.
The 31-year-old from Pyongyang stuttered backwards following his first vault - a piked double front somersault with half twist. The effort earned him 15.616.
He also stepped backwards from his second vault.
But there was so much difficulty packed into his Tsukahara full-twisting double back effort - a skill which he invented and is named after him - that the flawed landing did not affect his score too much and he was awarded 15.766.
Ri beat Denis Abliazin by 0.175 of a point. It was the Russian's second medal of the day after he collected bronze on the rings.
Japan's Kenzo Shirai, who missed out on a medal on his signature floor exercise event on Sunday, won bronze with 15.449. He edged out 35-year-old Romanian Marian Dragulescu on the tie-break rule after both earned the same average score.
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