Bidhya Sagar Das, 33, believed to be children's father, had been on the run after the toddlers were attacked on Saturday, in what police are describing as a suspected "domestic" incident.
Police have charged a man with murder following the death of a one-year-old boy in Finsbury Park.
Officers found the children at the address with critical injuries and they were taken to an east London hospital, where the boy died in the early hours of Sunday morning.
Das is expected to appear before Thames Magistrates' Court in London later on Tuesday.
A post-mortem examination in relation to the boy is due to take place later.
"Despite the best efforts of medical professionals a baby boy sadly died in the early hours of this morning".
Residents living nearby the Wilberforce Road flat where the twins were found said they heard the mother, named locally as Cristinela Datcu, screaming "My kids, my kids" shortly after 11pm on Saturday.
She later saw two young children being carried out of the building, with one held very close to a member of the emergency services. He lived with his Romanian girlfriend at the flat, which is now a crime scene.