The County Durham youngster's condition had deteriorated significantly in the past few days, and his parents had already announced he had become unresponsive.
He passed away at home at 1.35pm on Friday.
A message posted on Facebook page Bradley's Fight read:
"My brave boy went with the angels today 07/07/17 at 13:35, in Mammy and Daddy's arms surrounded by his family.
"He was our little superhero and put the biggest fight up but he was needed elsewhere. There are no words to describe how heartbroken we are. Thank you everyone for all your support and kind words.
"Sleep tight baby boy and fly high with them angels."
Bradley, his parents and elder brother recently enjoyed a final holiday together on the Yorkshire coast, where they were welcomed by visitor attractions such as Scarborough Sea Life Centre.
The Sunderland fan has also been a mascot at several of the club's matches, as well as England games.