The boy, named by the Evening Standard as Edward Gabriel Popadiuc, died on Friday afternoon after plunging from the fourth-floor of a building in Bridge Court, Harrow, north west London.
The incident came around 24 hours after an 18-month-old boy died following a fall from a ninth-floor "faulty window" at a block of flats in Tottenham, north London.
Edward's devastated father Alexandru Popadiuc told the paper: "I don't want to cry anymore, I do it all day and all night. He is our angel now.
"He was the best kid in this world. He had lots of energy and used to smile all the time."
A GoFundMe page to cover funeral costs and take the child's body back to Romania has so far raised more than £13,000.
One neighbour told the paper his window catches were "very flimsy" and said he had complained about it, while another, Anton Jesuthsan, said police had carried out checks on his window locks.
A Harrow council spokeswoman said: "We cannot comment on this incident at this moment while investigations are ongoing.
"The death is not being treated as suspicious."
Harrow Council does not own or run the building and it is not immediately clear which organisation does.
A Scotland Yard spokesman said no-one has been arrested and inquiries continue.
He said: "Police were called by the London Ambulance Service at 13:10hrs on November 1 to reports of a child falling from height from a residential building off Stanley Road, Harrow.
"Officers, the London Ambulance Service and London's Air Ambulance attended and found the child in a critical condition.
"The child, a three-year-old boy, was taken to a north London hospital.
"Despite the efforts of emergency services, he died at 14.44hrs."