Daley ended with a total of 521.10 points from his six dives, just over 43 points behind China’s Bo, who qualified top with of 563.55 points.
Yue finished second, 23 points adrift of compatriot Bo, while American David Boudia qualified third, 10 points ahead of Daley.
But there was disappointment for Australian defending champion Matthew Mitcham as he departed the Aquatics Centre in tears after missing his fifth dive and finishing down the standings in 13th.
The 18-year-old Daley said he was satisfied after qualifying into the final of the 10 metres platform at the London 2012 Olympic Games.
And Daley put his struggle in Friday night's preliminary round, when he just snuck into the semi-finals in 16th, down to the tight, changeable nature of diving, and insisted that any medal in the individual event is a huge success.
"That's diving for you - anything can happen," said Daley.
"David Boudia, from the USA, and I both qualified near the bottom for the preliminaries, but we are near the top of the table. The Chinese have been very consistent, though.
"It is sad to see Matthew Mitcham go out. I am not just diving for a bronze medal - bronze is almost gold as the standard of diving is so high."
Daley admits he is aware of the improvements he needs to make if he is to medal or better his seventh place from Beijing 2008.
But he intends to relax as he prepares for the biggest night of his career to date.
"There are a lot of things that I know I can do better,” he said. “For example the back twist and arm stand, so I hope to improve my score even further.
"I will go back, take a nap, chill, have lunch and write my diary about what happened in the semi-final."