The pair, who began training together last October, clinched only GB's eighth Olympic diving medal after pipping Germany to third place in a tense finish.
China's Lin Yue and Chen Aisen, the pre-competition favourites, won gold by a comfortable margin.
United States pair David Boudia and Steele Johnson claimed silver.
Daley is one of Britain's most recognisable Olympians after competing at the Beijing Games in 2008 aged 14 and then winning bronze in the 10m platform under intense pressure in his home Games in London in 2012.
While the 22-year-old is better known for his individual exploits, he and 19-year-old Goodfellow were fancied to win a synchro medal after taking European silver in May.
Tom Daley and Dan Goodfellow may not have been partners for long, but they have both been on fast-forward in terms of their development and rock-solid in their teamwork. |
There is trust there born of shared living quarters and long training sessions; while Daley might seem like the oldest 22-year-old in the GB Olympic team, he has found fresh enthusiasm and drive at his third Olympic Games in Goodfellow's less storied skills. |
With a score of over 84 points needed, the British duo waited anxiously before leaping into the pool in celebration when the score of 89.64 came up.
"Going into the last round there's an intense pressure in any competition, but when it's the Olympics it multiplies by a million," said Daley.
Goodfellow added: "I was nervous. But when we first started we knew there would be pressure. And we knew we'd be the last divers to go.
"We just kept our nerve and stayed in the moment."
British pair keep composure
Daley and Goodfellow, who moved in with his older team-mate as a lodger before the Games, put themselves in medal contention from their first dive.
They were joint third in the standings after round one, remaining in the bronze medal position following their second and third dives.
A loose dive saw them drop to fifth after round four, but they moved back into third with a forward four-and-a-half-somersault dive described by BBC Sport expert Leon Taylor at the time as their "best of the day".
They then trumped that with their final effort, keeping their composure to secure a sixth-round score only bettered by the Chinese and Americans.
Fuente:http://www.bbc.com/sport/olympics/36685698