The teenager, who cannot be named, denied attempting to murder Vincent Uzomah at Dixons Kings Academy, in Bradford.
But he admitted a charge of causing grievous bodily harm with intent – a plea prosecutors at Bradford Crown Court said they accepted.
Mr Uzomah had only been teaching at the school for a few weeks when he was attacked by the teenager as the lesson began at the start of the school day on 11 June.
It is understood the defendant argued with the teacher over a mobile phone after Mr Uzomah asked him to hand it over.
During the confrontation, the 50-year-old teacher was stabbed once in the stomach by the teenager, who immediately fled the school grounds, scaling a fence.
He was stabbed with a kitchen knife the boy had brought from home.
The boy was arrested by police in the city centre following a six-hour search – an incident caught on mobile phone video by bystanders.
Yesterday, the boy sat in the dock flanked by two security guards. He wore blue jeans, grey shirt and a black Puffa-style jacket.
He said “Yes, sir” when he confirmed his name and spent much of the rest of the 11-minute hearing with his head bowed.
No details of the stabbing incident were mentioned in court yesterday but Judge Jonathan Durham Hall QC said: “This is a very troubling case.”
He said the boy was “undoubtedly a very troubled young man” and said that Mr Uzomah was “a very brave and compassionate victim”.
Judge Durham Hall said that a psychiatric report and a pre-sentence report needed to be prepared before sentencing.
He said he agreed with the Crown Prosecution Service’s decision not to proceed with a charge of attempted murder, saying it would be very difficult to prove the defendant had an intention to kill.
As the boy left the dock the judge thanked him.
He said: “Your plea has been noted, very proper, at a very early stage. Thank you.” The boy was watched by two members of his family from the public gallery as he was led away.
Mr Uzomah did not attend court.
After the incident at the school, Mr Uzomah was rushed to hospital but was able to be released a few days later following surgery.
He later issued a statement thanking people for their support.
He said: “I wish to express my heartfelt gratitude to God and to everyone for all the support that myself and family have received during the course of the [most]traumatic event of my life.
“It has been 12 days since this event occurred and I thank the Lord Jesus for sparing my life.”
Mr Uzomah, who has worked as an extra on soaps Emmer-dale and Coronation Street, also thanked the doctors and nurses who helped him and the staff at Dixons Kings Academy.