The American only climbed into the world top 15 in early July, which put him into contention for one of his country's four spots. But he still had two Americans, Dustin Johnson and Jordan Spieth, ahead of him.
When both said they would not go to Rio over health concerns, Kuchar squeezed by to take the final spot.
And he's so glad he did.
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"I was just on the outside and barely qualified," he said after finishing three strokes behind Justin Rose, golf's first Olympic champion in 112 years on Sunday.
"I have never been so proud of a third-place finish in my life. I can assure you it is the happiest I have ever been finishing third."
He said he drew inspiration from the United States' performance in the tennis bronze medal match in men's doubles that he attended on Friday.
"We were sitting in the players' box and Team USA wins and the boys come running and jumping up into the box," Kuchar said.
Kuchar, 38, adds a bronze to an impressive resume that includes three seven PGA Tour wins and three appearances in both the Ryder Cup and Presidents Cup. A golf major still eludes Kuchar, however.
An avid table tennis player who has faced off before against Olympians in friendly matches, Kuchar said he is hoping to buy an Olympic ping pong table when he gets back to the United States.
(Reporting by Liana B. Baker, editing by Neil Robinson)
