Bidhya Sagar Das, 33, was wanted by police in relation to a “domestic incident” at a flat in Wilberforce Road, near Finsbury Park, north London, on Saturday night.
Both toddlers were found at the flat with critical injuries and were rushed to an east London hospital.
The boy died in the early hours of Sunday morning while the girl remains in a critical condition.
Mr Das, of Wilberforce Road, was charged in the early hours of this morning and is set to appear in custody at Thames Magistrates' Court.
Detective Chief Inspector Dave Whellams, who is leading the investigation, said shortly after the incident: "This is clearly a tragic incident, and our thoughts are with the family of the two young children.
"Despite the best efforts of medical professionals, a baby boy sadly died in the early hours of this morning.
"A baby girl currently remains in a critical condition and is receiving specialist medical care.
"I would still like to hear from anyone who may have any information regarding this terrible incident."
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