Hull, famous for his antics with his puppet Emu, tumbled from a ladder outside his bungalow in Winchelsea, East Sussex, in 1999.
The 63-year-old was pronounced dead on arrival at hospital with a coroner later recording a verdict of accidental death.
Speaking to John Cleese on the latest episode of his Rosebud podcast, Brandreth said: “I killed a man. “It was Rod Hull, the emu man.”
The 76-year-old former GMB presenter revealed that Hull had been complaining to him about his awful TV connection and he “encouraged” him to “get a ladder” and climb on the roof.
Brandreth said he feels responsible for his friend’s death after he took his advice while watching a Champions League match between Manchester United and Inter Milan, at half-time.
He explained how he had been at the theater with Hull on the day of his death, a day he said was struck by “terrible, terrible weather”.
Brandreth added: “He was sitting next to me, and he was complaining all through the show – he was interrupting the show almost – going on about how he wanted to get home because he wanted to watch the football, but his Sky aerial wasn’t t transmitting properly.
“And I said, ‘Don’t moan about it, if you want to watch the television get a ladder out, climb on to the roof, and fix it Rod.’
“And after the show, in this stormy weather, he went home, he got out a ladder, he climbed the ladder, and he tried to fix the aerial.
“Unfortunately the wind was very great and he fell backwards off the ladder and killed himself.
“So I wasn’t actually there, but I’d encouraged him.”