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Jonty Bravery, who was 17 at the time of the incident, said he carried out the act because he wanted to be on the television news.
He pleaded guilty to one count of attempted murder at London's Old Bailey court on Friday, the Crown Prosecution Service (CPS) said in a statement.
The victim, who was visiting Britain with his family, fell five floors and was found on a fifth-floor roof.
His mother was heard by witnesses screaming: "Where's my son? Where's my son?"
The boy survived but suffered a bleed to his brain and a number of fractured bones, the CPS said.
Bravery, who was arrested shortly afterwards, told police he had planned to hurt someone at the museum be on television, the CPS said. He was only named in the media in October after he turned 18.
"This devastating and shocking incident at the Tate Modern on August 4 of this year changed the lives of Bravery's young victim and his family forever," prosecutor Emma Jones said.
"The boy was singled out by Bravery who threw him from the viewing platform intending to kill him. That he survived the five storey fall was extraordinary."
He will be sentenced on February 17 next year.
Bravery, who has autistic spectrum disorder, obsessive compulsive disorder and was likely to have a personality disorder, has been held at Broadmoor Hospital since mid-October, the BBC reported.
The victim's family said the injured child still needed intensive rehabilitation and has not recovered mobility in all his limbs or cognitive capacities. He was constantly awoken by pain but could not communicate that, they said in a statement released by police.
"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," the family said.
"We are exhausted, we don't know where this all leads, but we go on."