Waller published seven books, but Bridges was his most famous, selling 12 million copies in 35 languages.
The romantic novel was adapted into a 1995 film starring Clint Eastwood and Meryl Streep, who was nominated for a Best Actress Oscar in the role.
The bittersweet 1992 love story was also adapted into a Broadway musical.
Bridges, which Waller said he wrote in only 11 days, tells the story of a National Geographic photographer who woos an Italian war-bride married to an Iowa farmer, after she agrees to help him photograph the region's famous covered bridges.
The Eastwood-directed movie grossed $182m (Â£150m) worldwide, and the book remained on the New York Times bestseller list for more than three years.
The novel made Waller a multimillionaire and turned Madison County, Iowa into an international tourist attraction. Many thousands flocked to wed on its celebrated bridges.
After his success, the writer moved from his native Iowa to a remote part of Texas and divorced his wife of 36 years.
His other books include Slow Waltz in Cedar Bend, Border Music, Puerto Vallarta Squeeze, and A Thousand Country Roads, which was a sequel to Bridges.
Robert James Waller, the author of best-selling book The Bridges of Madison County, has died in Texas at the age of 77, his agency said.