The 6-year-old victim survived but suffered horrific injuries, including a bleed on the brain, broken arms and legs and fractured spine. He has been left unable to move, eat properly or speak.
His condition has improved but he has not yet recovered mobility in his limbs or cognitive capacities.
The Crown Prosecution Service today told the court Bravery told police he planned it in advance and wanted to hurt someone during his visit to the Tate Modern so he could be on TV.
The teen, who has autistic spectrum disorder and obsessive compulsive disorder, managed to escape his minders who were accompanying him on the trip to the art gallery.
Bravery appeared at the Old Bailey via video link from Broadmoor Hospital.
He laughed out loud before admitting to trying to murder the young boy.
Asked to confirm his identity, Bravery said: "Yes I am that man."
Asked how he pleaded to one charge of attempted murder, he replied: "I plead guilty, guilty yeah."
He repeatedly shook his head and rolled his eyes during court proceedings and attempted to interrupt by shouting "not correct".
His lawyer says he is likely to have a personality disorder.
In a recent statement, the victim's parents said the boy "still needs intensive rehabilitation since he hasn't recovered mobility in all limbs or cognitive capacities".
"He is constantly awoken by pain and he can't communicate that pain or call our to hospital staff," they wrote.
'Life stopped for us four months ago. We don't know when, or even if, we will be able to return to work, or return to our home, which is not adapted for a wheelchair.
"We are exhausted, we don't know where this all leads, but we go on.
"We wish to thank all of the people, family and friends who have supported us throughout this horrific experience."
They had previously revealed the extent of their son's suffering in a message on a GoFundMe page set up to support the family.
"Our little boy doesn't know any more how to speak, to eat or to move his body but he begins to do his best to move his tongue, his right arm and hand.
"We see his efforts. He is very brave. He keeps on smiling and reacting to our jokes.
"We begin to see also, unfortunately, his suffering... he cannot manage to eat or swallow a little bit of yoghurt for instance... and he wants so much to be able to do it."