Principal of Capital City Academy, Alex Thomas, said the school is deeply saddened by the death , which happened at around 3.30pm on Monday (January 23).
The victim, Quamari Barnes, was stabbed in Doyle Gardens and was rushed to hospital where he died.
A 15-year-old has been arrested in connection with the murder, but Mr Thomas said the teen is not connected with Capital City Academy in any way.
In a statement released on Tuesday evening (January 24), Mr Thomas said: “Capital City Academy has been overwhelmed by the kind words and messages of support received today following the tragic incident after school yesterday, which led to the death of a 15-year-old boy.
“We are deeply saddened by this death; it is undoubtedly a tragic loss of life.
“Our thoughts and prayers are with his family and those who knew and loved him.
“He was positive about learning and had a bright future; he will be greatly missed by his many friends and the entire school community.
The statement went on to say: "Capital City Academy will continue to provide support to students and staff at the school from councillors in the coming days and weeks.”
A teen was arrested in connection with the fatal stabbing at an address in South Norbury at around 1.30pm on Tuesday.
He remains in custody.
Tributes to Quamari were left at the school gates including a large Jamaican flag, Bob Marley quotes and a painted portrait of Quamari.
Capital City Academy has around 1,200 students, according to the most recent Ofsted report in 2015 and was rated "good" overall by inspectors.
Anyone with information is asked to contact the Metropolitan Police incident room on 02083580200 or via 101.
You can also tweet @MetCC on Twitter or pass information anonymously to Crimestoppers on 0800 555 111.
Keep up to date with the latest news in west London via the free getwestlondon app.
You can even set it to receive push notifications for all the breaking news in your area.