The pair struck up a strong bond while Defoe was with the Black Cats.
And the 34-year old, who was speaking at his unveiling at Bournemouth, could not hold back tears when he revealed Bradley did not have long to live.
"It has been difficult. I have kept this in for so long," Defoe said.
"I have tried to be strong for my family and his family but I don't know how to put into words how I feel. It's a special time, having that special time with Brads.
"The first moment I met him I could not believe he was the young kid who was ill because he ran over to me. From that moment, there was an instant connection.
"I knew he would be mascot but I hadn't seen a picture and he just ran over to me. His energy in the changing rooms, bossing the other kids about - a great character.
"I speak to the family every day and I was with him a few days ago. It was tough to see him suffer like that.
"I felt like I was prepared for it after what I went through previously with my dad [Defoe's father Jimmy died of throat cancer in 2012]. It was so tough to see a kid of that age going through it for so long.
"It's got to the stage where he is obviously struggling. I can say it is probably a matter of days. He will always be in my heart for the rest of my life.
"We are there for the family, even going forward. It is difficult. It puts stuff into perspective.
"There is not a day that goes past where I do not wake up in the morning and check my phone or think about little Bradley because his love is genuine and I can see it in his eyes. It is special."