The sports star, who was 17 at the time, said he thought his father Robert was “invincible” until the moment of his death aged 40 from brain cancer in 2011, a year before Daley competed in the 2012 London Olympics.
He told Radio 4’s Desert Island Discs how he was called back from Fort Lauderdale, Florida, by his mother when she knew his father had just a few days left to live.
He told the programme’s stand-in host Lauren Laverne: “I get home and I see my dad in a hospital bed in the living room. As the days went by his condition started to deteriorate.
He continued: “It was the next day, when all of our family and friends were around and he had gone unconscious. We were watching his chest.
“I was holding his hand as he stopped breathing.
“It wasn’t until he stopped breathing and he was dead that I finally acknowledged that he wasn’t invincible, that he wasn’t going to be there to teach me to drive, to fill up my first pint, to be able to watch me win an Olympic medal, to see me get married, to see me have a kid.
“All those things. Because 40 years old is such a young age to die. I was 17, my brother was 15 and my younger brother was 12.
Daley and his husband Dustin Lance Black welcomed their first child, a son, in June via a surrogate.
They named him Robert Ray, after Daley’s father.
Laverne is filling in for Desert Island Discs presenter Kirsty Young, who is taking a step back for several months as she is suffering from a form of fibromyalgia.
Tom Daley is on Desert Island Discs on BBC Radio 4 on Sunday at 11.15am.