Speaking just before hundreds of fans filed into a small space at the back of WHSmith, he said: "It's crazy to say the least, honestly, about a thousand people are here today and they've had to shut the queue because there were too many people turning up.
"It's amazing to think that people have actually camped out since before 11pm last night."
The diver had dedicated his Olympic medal to his father, Rob, who died of cancer aged 40 last year.
"I think my Dad would think this is quite funny actually," Daley said. "He'd probably go around, running around the queues actually winding people up, like saying 'Oh, he's gone home' things like that, he had that kind of sense of humour, so I think he would be enjoying it a lot."
Daley's book My Story follows his diving background and success, the attention he has received since competing at the Beijing Olympics and the loss of his father.