Martyn Turley, aged 58, fatally stabbed 34-year-old barber Stuart Roe in Halesowen last December.
Turley pleaded guilty days into his trial at Birmingham Crown Court but the motive for the murder has never been revealed, according to West Midlands Police.
Mr Roe, who ran Mr Trim's barbers in Quarry Bank high street, was stabbed multiple times after a night out and was found by a member of the public at around 1.30am on December 30
He was pronounced dead at the scene in Springfield Drive, Coombeswood, near Blackheath.
Mr Roe had been out drinking at the Britannia Wetherspoon pub in Halesowen Street, Rowley Regis, earlier the previous evening, while his killer had also been out drinking in Rowley Regis but with separate groups of people, according West Midlands Police.
Detectives say Turley and MR Roe did not cross paths and were not previously known to each other but headed home from their respective nights out at around the same time.
Both took separate routes before coming face to face for the first time on Olive Hill Road, near Shell Corner, at around 1.20am.
Less than 15 minutes later Mr Roe was fatally stabbed on nearby Springfield Drive.
But the circumstances remain a mystery as the CCTV footage has no sound.
CCTV on Olive Hill Road showed Turley grabbing a metal bar from a skip, while Mr Roe armed himself with a rock.
But police say the pair parted ways and went to separate properties before coming back out and onto Springfield Road.
When 58-year-old Turley, from Whitehouse Street, Tipton, was arrested at around 4pm the same day police found a pair of blood-stained trousers in the address.
Police seized them for examination by forensic scientists and DNA on the clothing was found to match that of Mr Roe's.
Police used this evidence, CCTV footage and witness testimonies to build a case against Turley but to date the motive for Mr Roe’s murder remains unclear, say investigating detectives.
Detective Inspector Caroline Corfield, from West Midlands Police, said: "This was such a shocking and appalling crime committed by Turley, and one where he has shown absolutely no remorse.
"There is seemingly no reason for the attack, and to date he’s offered no explanation as to why he did what he did.
"That said, no motive can ever justify the senseless murder of a young man, or undo the pain and suffering inflicted on Stuart’s family.
“Thankfully Turley pleaded guilty, and now faces the consequences of his actions.
"I hope his subsequent prison sentence provides some solace for Stuart’s family and friends.”
In a statement released today Mr Roe’s family said: “We’re relieved at today’s outcome, and we’d like to thank the police for all of their hard work and dedication which has left our son’s killer with no choice but to plead guilty to his murder.
“Stuart will always be missed, and although nothing will ever bring him back we’re pleased that we’ve finally got justice for what happened to him.”
Tributes poured in for Mr Roe following his death, with a Go Fund Me page raising £5,320 towards his funeral.
The page stated: "Stuart Roe was 34 years old, he was an avid Wolves fan and was a season ticket holder with his dad as a young child.
"He was a fantastic barber and had his own shop called Mr.Trim on Quarry Bank high street.
"Stuart was a loveable, kind, generous, friendly, caring, sociable person and a friend to many.
"This is a tragic loss to everyone who knew and loved him.
"He was a loving son, brother, uncle, nephew, grandchild and cousin."
Turley will be sentenced at Birmingham Crown Court on December 17.