The pre-tournament favorites kept Kasparov on the top board throughout the two-week event, and finished with 37.5 points out of a possible 56, beating Bosnia by 2 1-2 points. The team finished with a 3.5-0.5 rout of Germany on Thursday.
Bosnia drew 2-2 with Bulgaria on Thursday and finished alone in second for the silver medal.
The junior Russian squad finished with the bronze after drawing 2-2 with England.
Although the two were tied entering Thursday's final round, England needed to beat Russia outright to be assured a medal.
Jonathan Speelman won the final match for England to earn the draw, but the Russians were awarded the bronze medal because of their superior sum of opponent's scores in a tie-breaker.
The U.S. team needed to win by three points to have a chance at the bronze, but managed only a 2.5-1.5 defeat of Yugoslavia and finished in a tie for fifth with the Dutch with 34 points.
In the women's division, Georgia was declared the champion when all three boards were agreed drawn after only 10 minutes against Vietnam.
The draw gave Georgia 32 points, one more than Hungary despite its 3-0 victory over Kazakhstan.
China finished third ahead of Romania, again using the tiebreaker as in men's play.
"The competition was very difficult but at the last moment fortune smiled on us," Kasparov told Russian television.
One hundred and twenty-four men's teams and 81 women's teams took part in the Olympiad, held every two years.
The world of top-level chess was torn apart in March 1993, a few months before Kasparov was due to defend his World Chess Federation (FIDE) championship crown against Britain's Nigel Short.
The two players walked out of FIDE when it put through a plan to hold the championship in Manchester, England. They founded the breakaway Professional Chess Association (PCA) and staged their match themselves in London. Kasparov won. (AP, Reuters)
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