David Gomoh, a 24-year-old marketing graduate who worked for the NHS, was stabbed to death in Newham just days before the funeral of his father, who died of a coronavirus-related illness.
The Metropolitan Police said officers arrested a 19-year-old man in Stratford on Friday afternoon and a 17-year-old boy was subsequently arrested at a home in Telford, Shropshire, on Saturday morning.
Both teenagers remain in custody.
Police added that Mr Gomoh was attacked on Freemasons Road, Newham, at about 10.25pm on Sunday 26 April, just seconds after leaving his home.
A post-mortem examination found the cause of death was stab wounds to the chest and abdomen.
Detectives investigating the attack said they believed those involved left the scene in a stolen silver Dodge Caliber, which was found abandoned at about 10.30pm on Lincoln Road, Newham, just a few minutes drive away from Freemasons Road.
The car had been stolen in Dagenham on 16 April and was on cloned plates when it was found, police said.
Anyone who was in the area or anyone who remembers the car, before or after the attack, has been urged to contact the Met Police.
Detectives added that the evidence so far suggested Mr Gomoh was murdered in a “totally unprovoked attack” as there was nothing in his background which gave any reason for why he was singled out and assaulted.
Mr Gomoh was a keyworker helping to keep NHS staff supplied with essential equipment during the coronavirus pandemic.
His mother works as a nurse and his father had recently died unexpectedly from an illness related to Covid-19.
“David’s family are going through unimaginable torment. Within days his mother has seen the death of her husband and son; his sister has lost her father and brother. Both are now heartbroken,” Detective Inspector Tony Kirk, from the Met's Specialist Crime Command, said.
“David was a young man who had worked hard to put himself through university and, like his mother, worked hard for the community in the NHS.
“At this time we believe the only thing David did to be murdered was walk down a street. He was apparently approached by a group of men wearing masks and stabbed multiple times in a ferocious assault.”
Mr Kirk added: “David and his mother, who have done so much to help the community, now need the public to come forward and tell us what they know.”
Anyone with information on the incident should contact police via 101 or via Twitter @MetCC, quoting CAD 8371/26APR, or contact the police incident room on 020 8345 3985.
Alternatively, anyone who wants to give information anonymously can contact the independent charity Crimestoppers on 0800 555 111 or online at crimestoppers-uk.org.
Additional reporting by PA