Dwayne Stewart-Akers, 38, was found guilty last Friday of the murder of Ampadu in February.
On Thursday, he was sentenced to life in prison and he will serve a minimum of 25 years in prison.
If released, he will remain on licence for life.
Detective Chief Inspector Claire Hine, the lead investigator, said: “This was a violent and unprovoked assault on a man who was – up until that moment – friends with the defendant.
“The ferocity of the attack was clear to see and left Jack Ampadu with a number of injuries which proved fatal. Shortly after the murder, Stewart-Akers pretended to be a victim but his ruse was identified and he was arrested by quick thinking officers.
“Our thoughts remain with Jack’s family, I can only hope that seeing the man responsible convicted and imprisoned will bring them some comfort.”
Police were called to a communal area at flats on Highgate Road at about 7.30pm on Monday 15 February.
They found 37-year-old Ampadu suffering from multiple stab wounds. Despite the best efforts of paramedics, he died at the scene a short time later.
A post-mortem examination held at St Pancras Mortuary established the cause of death as a stab injury.
Stewart-Akers was stopped by officers at the scene at he tried to run away.
Detectives from the Specialist Crime Command launched a murder investigation.
They quickly established that Ampadu had been friends with Stewart-Akers. On the evening of the murder, he had gone to visit him but they had argued.
Ampadu left the flat but Stewart-Akers followed him onto the landing where he launched a ferocious attack with a kitchen knife.
A review of CCTV footage confirmed what officers had been told and captured the moment of the fatal stabbing.
A second man who was arrested was later released with no further action.