Robert Buckland, 18, was remanded for psychiatric reports until next month, when he will be sentenced. His victim, Alison Kennedy, 28, miraculously survived the attack in which the five-inch-bladed Bowie-style hunting knife had to be removed from her head.
Buckland said he had wanted to snatch Miss Kennedy's handbag but had thrust the knife into her skull in a rush of anger, intending to kill her. When she turned and rose from her seat, holding the knife in her head, Buckland ran away scared and tried to jump from the train.
The Old Bailey was told he suffered from a severe psychopathic disorder from early childhood which exploded into violence on occasions. At school, he had fantasised about stabbing a woman in the head.
Buckland had admitted wounding Miss Kennedy, who was travelling to visit her sister on the Waterloo to Guildford train in March last year. But he denied attempted murder.
He had left home at 16 after trouble with his stepmother but by March last year he was fed up sleeping rough and begging. He was on his way to Guildford to find a bed for the night. Miss Kennedy was on the same train visiting her sister.
Among the few possessions Buckland had was the knife and a hammer he said his father had given him. He said he had them so he could break into premises to steal and feed himself.
He took out the hunting knife when he was three feet behind Miss Kennedy.
He told the court: "I put my hand on the grip exactly like you see in a horror movie. I took the knife out of my pocket and raised my arm up in the air.
"Then a big rush of anger. As I pulled my arm down, it all came out. I think all the stress and frustration had all been released in that blow. I had not planned to dispose of it in that way - that was just the way I was feeling," he said.
Afterwards he said he was shocked by what he had done. "She stood up. I did not know what she was going to do. To be quite honest, I was scared of her. I ran through the carriage. I saw her stand, one hand on her head, staggering down."
Miss Kennedy, a charity worker from Northern Ireland, said she thought she was going to die. She will never fully recover from the assault and is to have more surgery .
Speaking outside the courtafter the verdict, she said: "I feel a great sense of relief at the result and a great sense of satisfaction to be here to see it for myself.
"I would like to say thanks to everyone who helped me and I am looking forward to getting on with my life."
Surgeons originally thought Miss Kennedy would die from the massive knife wound. She still needs an operation to repair bone deficiency and has suffered extensively from deep psychological trauma.
Dr Adrian Casey, the surgeon responsible for removing the knife from Miss Kennedy's head, said: "To survive relatively intact from an injury of this kind is nothing short of a miracle."
"When she came to across to us she was lying on a trolley with a knife coming out of her head. The amazing thing was she was awake and alert despite this horrific injury.
"We put her to sleep under general anaesthetic and then in theatre we opened up the wound where the knife had shattered the skull and we drilled with a high-speed drill around the knife so we had full access to the brain and then I cautiously removed the knife."Reuse content