Devoted father Peter Duncan, 52, suffered a fatal chest wound as he walked into Eldon Square shopping mall in Newcastle, close to a Greggs outlet, on August 18.
The youth, who cannot be named by the media due to his age, appeared via a videolink from HMP Wetherby to admit murder, as well as stealing screwdrivers from Poundland and possessing an offensive weapon.
Northumbria Police last month said the murder was unprovoked and described it as a "chance encounter", and they quickly arrested a group of teenagers in the hours after the attack.
The day after the murder, Mr Duncan's family said: "Peter was a kind and caring man who was always first to help others.
"He was a devoted father, husband, son, brother, uncle and friend and loved by all who knew him. His death will leave such a huge hole in our lives and he'll be deeply missed by us all.
"Words can't quite describe what life will be like without him.
"He had so much of his life left to live and he'll be in our hearts and thoughts every day."
The murderer wore headphones for the case which was linked to Leeds Crown Court where the judge and prosecution barrister were sitting, and to Newcastle Crown Court where his defence barrister was present.
He will be sentenced in December after psychiatric and psychological reports are prepared.
Judge Andrew Stubbs QC told him: "The appropriate form and length of your sentence will be decided at the start of December when the necessary reports have been prepared and served on the prosecution and defence."
At a previous hearing, it was said that 52-year-old Mr Duncan was "simply in the wrong place at the wrong time" when he crossed paths with the teenager who has a history of violence and carrying knives.
Mr Duncan worked as a lawyer for a multi-national maritime firm and lived in the Benton area of the city.
At a previous bail hearing for the youth, prosecutor Kevin Wardlaw said Mr Duncan and his killer came into contact with each other by chance at the entrance to the shopping centre, when they were walking in opposite directions.
The teenager had stolen the screwdrivers and was looking for another youth with whom he had previously argued about cigarettes.
Mr Wardlaw said: "The deceased raised his arm to let the defendant get past.
"It is captured on CCTV footage.
"The defendant took exception to that, took hold of the deceased and a struggle ensued."
Mr Duncan managed to push the teenager off, at which point the youth stabbed him once in the heart.
He managed to walk a short distance away before he collapsed to the floor.
CCTV camera tracked the youth's movements through the city centre and the murder weapon was found later.
At the previous bail hearing, Newcastle Crown Court heard he had 17 convictions for 31 offences between 2017 and 2019, including an incident where he grabbed a knife during a family argument and an occasion where the threatened a driver with a blade after he was challenged about drinking alcohol on the bus.
At the time of the murder, the boy was on bail for affray.
Following the case, Detective Chief Inspector Jane Fairlamb said: "This was a shocking incident in which a much-loved family man was murdered in an unprovoked attack after a chance encounter.
"I want to make it crystal clear it can never be acceptable for anyone to carry a weapon on our streets - as this case highlights the consequences can be truly devastating.
"I would urge anyone who thinks otherwise to think again.
"Not only could you destroy someone else's life and those of their loved ones - but also think of the impact on your life and that of your family and friends.
"I can assure you if you are caught with a weapon you will be dealt with robustly and put before the courts."