The Olympic medal is the first for the Bryans, who have won all four Grand Slam championships and 48 tournament titles. They were seeded No. 1 in Beijing but lost to Roger Federer and Stanislas Wawrinka of Switzerland in the semifinals Friday.
Llodra and Clement were coming off a 19-17 third-set loss in the semifinals.
The U.S. tennis team will win one other medal. Venus and Serena Williams play for the women's doubles title Sunday.