Rohler, from Germany, made a 88.26m throw in his second attempt and finished fourth while Beijing worlds victor Yego was eliminated after the first three rounds. Washington will get a gold medal.
"I gave it everything", said Farah, who is moving up to the marathon.
"Mo has many victories but now I have one".
Farah, who had already won the 10,000m last week, had not lost a final in 2,176 days, and collapsed to the track after the race and covered his face before being hauled to his feet. Defending champions Jamaica clocked 42.19 for the bronze.
The 34-year-old couldn't hide his disappointment after crossing the line in the race, which took place in the same stadium in which he won two Olympic golds five years ago.
He had been hoping for one final coronation in front of an adoring home crowd.
Pamela Dutkiewicz of Germany secured the best result of her career with bronze medal in 12.72.
"It's been wonderful. It's been a long journey but it's been incredible", said Farah who was embraced by his fans as he made his way around the stadium on a lap of honour. Germany's Rico Freimuth, bronze victor two years ago in the Beijing worlds, took silver in 8,564 points and his compatriot Kai Kazmirek won bronze in 8,488.
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Predicted line up versus Stoke City
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