The England striker struck up a close friendship with Bradley during his time at Sunderland.
He died on Friday, aged six, leading to tributes from all across the game.
And Defoe, who visited Bradley in his dying days, told his friend in an statement, accompanied by a montage of pictures of the two: "I will always carry you in my heart".
"Goodbye my friend, gonna miss you lots," he wrote.
"I feel so blessed God brought you into my life and has some amazing moments with you and for that I'm so grateful."
The pair first met when Bradley was mascot for Sunderland as his family started their campaign to raise awareness for the rare disease.
"I'll never forget the way you looked at me when I met you for the first time, the genuine love in those cute eyes
Really finding it hard to find words to express what you mean to me."
Defoe, who left Sunderland after their relegation to join Bournemouth, broke down at his unveiling at his new club this week when asked about Bradley.
Bradley and Defoe were pictured snuggled up together at the youngster's home in Blackhall, County Durham last week after the little boy had a party in bed as a way of saying goodbye.
"Your courage and bravery will continue to inspire me for the rest of my life," he added.
"You will never know what a difference you made to me as a person
God has you in his arms and I will always carry you in my heart.
"Sleep tight little one
My best friend."
In a statement on the family's Facebook page on Friday, Bradley's mother Gemma Lowery said: "My brave boy has went with the angels today 07/07/17 at 13:35, in mammy and daddies arms surrounded by his family
"He was our little superhero and put the biggest fight up but he was needed else where.
"There are no words to describe how heart broken we are.
"Thank you everyone for all your support and kind words
Sleep tight baby boy and fly high with them angels."
Source : PA