In a reversal of their Olympic bout four years ago, Kim defeated Bischof to win the gold medal Tuesday in the 81-kilogram event at the London Games. Kim dominated from the start, throwing Bischof twice and often attacking, even when both were locked in grappling moves on the ground.
Bischof, who beat Kim for the gold at the Beijing Games, said the South Korean deserved the victory this time.
"He is much stronger and quicker now," Bischof said. "I think we have the correct champion."
It was South Korea's first judo gold medal of the games and adds to the country's judo tally: Teammate Cho Jun-ho won bronze in the lightweight men's division earlier this week.
Kim, the 27-year-old world champion, also paid tribute to Bischof. He said he didn't think his 32-year-old rival had aged at all since Beijing—at least athletically.
"He is such a great player and I'm very glad to have competed against him," Kim said.
The bronze medals were won by Ivan Nifontov of Russia and Antoine Valois-Fortier of Canada.
American Travis Stevens fought several grueling matches to make it to the semifinals, where he lost to Bischof. By that fight's end, Stevens had several bandages wrapped around his head. He lost in the repechage bronze-medal match to Valois-Fortier.
In the women's division, Urska Zolnir of Slovenia won the 63-kilogram event, defeating Xu Lili of China. Zolnir managed to throw Xu once in the match's first minute, which was ultimately enough to win.
She also won Slovenia's first Olympic judo medal at the Athens Games when she entered as a wildcard and took the bronze. Zolnir focused mainly on grappling moves Tuesday, pinning down her opponents throughout the day.
At 31, she was one of the oldest competitors in the division.
"You will not meet me in Rio," she predicted.
Zolnir said winning the gold came as a surprise even to herself.
"I did not expect the gold medal when I woke up this morning," she said, adding her confidence grew as she won more matches.
The bronze medals were won by Yoshie Ueno of Japan and Gevrise Emane of France.
Japan, which won judo gold Monday, had another disappointing day. The only medal Tuesday for the country that invented the sport was Ueno's bronze. So far, Japan has won one gold, two silver and two bronze medals.
Ueno acknowledged Japan expected more medals, but said her coaches had not said anything about it to the athletes.
"We still have tomorrow," she said.