Terrell Davis, 27, is said to have got into an argument while out shopping for his grandmother in Brixton at about 6pm on Sunday.
Despite the efforts of police and paramedics, he died at the scene.
Grammy-award winning 21 Savage, 28, who was born in Plaistow, east London before he moved to the US aged seven, shared a childhood picture of him with Mr Davis on Instagram.
He wrote: “Can’t believe somebody took you baby bro. I know I took my anger out on you I wish I could take that s*** back.”
Kyra Davis, their sister, said on social media: “I don’t even know what to say. My heart is in pieces. I love you more than words can say. Rest in perfect peace Terrell.”
Mr Davis, a drill rapper known as TM1way, had the same father as Atlanta-based 21 Savage.
A family source told MailOnline that Mr Davis had got into an argument with a former friend, who suddenly lunged forward and stabbed him. They said: “Terrell was a good guy, he used to live on the estate but had moved away.”
No arrests have been made.
In February last year, 21 Savage had been due to attend the Grammy awards where he had been nominated for record of the year for his Post Malone collaboration, Rockstar.
But he was arrested by US Immigration and Customs Enforcement which said he was a UK citizen who had unlawfully overstayed his visa. He was released with his hearing later postponed indefinitely.
A man, believed to have been in his sixties, was knifed to death at Kensal Green cemetery on Harrow Road at 2pm on Sunday. Cornelius Tully, 50, of High Street, Brent, has been charged with murder and was due before Harlesden magistrates’ court today.
On Friday night, Paul McCarroll, 45, was stabbed to death in Oaks Road, Kenley, near Croydon.