Oh had survived a nerve-wracking single arrow shoot-off against China's Dai Xiaoxiang to reach the final but left nothing to chance against the Japanese, closing out the victory in four sets.
Dai beat Rick van der Ven of the Netherlands to win the bronze, earning China their first men's individual medal.
Oh's win brought to an end South Korea's long wait for the individual title. The South Koreans have had the upper hand in the team competition, winning four of a possible seven, but the individual title had always eluded them.
The 30-year-old had tried to break into the mighty Korean Olympic team for more than a decade and said he just had to bide his time to make his dream come true.
"I was not as good at sports in my 20's, but now I've turned 30 and I want to keep doing sports for a long time," said Oh at a news conference.
"I was taking part in the national qualifications to participate in the Olympics since the Sydney Games.
"I always hoped to get to the Olympics and now my first dream has come true, and on top of that I have a gold medal so really I'm a very happy man."
Both individual gold medals went to South Korean athletes at the 2012 Games as Ki Bo-bae won gold on Thursday.
The Korean women also won their seventh consecutive Olympic team gold in London while their male counterparts had to settle for bronze after winning the team title at the Sydney, Athens and Beijing Games.
Japan's Furukawa had also come through a shoot-off in his semi-final and while he said he was initially disappointed to miss out on the gold he soon realised how special it was to earn an Olympic silver medal.
"Immediately after I lost the final I was regretting that I couldn't get the gold ... but after that I did some interviews and the sense of happiness gradually came to the surface and now I'm really happy."
Oh was part of the Korean trio that broke the team 72 arrow world record in the ranking round last Friday, but his team mates Im Dong-hyun and Kim Bub-min were the two favourites to vie for the gold.
However, world number two Im was stunned by the Netherlands' Van der Ven in the last 16 while Kim lost to China's Dai in the quarter-finals.
Dai was bitterly disappointed to miss out on the final and rued the fact all four of his matches on Friday had been decided in a shoot-off after the scores after five sets were tied.
"This is not what I wanted," he said. "I'm not here just to compete for that one last arrow."