Obina Ezeoke, 24, is accused of killing Annie Besala Ekofo, 53, and her nephew Bervil Kalikaka-Ekofo, 21.
Four other people, including a child, who were also inside the address at the time were not harmed.
A post-mortem examination into Bervil's death was conducted last week at Northwick Park Hospital Mortuary, concluding that the cause of death was a gunshot wound to the head.
The post-mortem examination for Annie has not yet been conducted and enquiries into both her and Bervil's death are continuing.
They were gunned down at a flat in East Finchley, north London, on Thursday shortly after 6.30am.
Scotland Yard said Ezeoke, of no fixed address, is to appear in custody at Hendon Magistrates' Court in north west London on Wednesday. The 20-year-old man remains on bail until a date in late October.
Bervil's mother, Maymie Botamba, who lost two family members in the shooting, paid tribute to her "perfect" son.
"He was my friend, my best friend, my everything," she said.