Seven-year-old Neon will have radiotherapy treatment, following surgery on a brain tumour, against his mother's wishes.
Specialists treating Neon accepted that there were side-effects to radiotherapy but said that without the treatment the youngster could die within a few months.
Mr Justice Bodey, who heard evidence at a hearing in the Family Division of the High Court in London, said radiotherapy treatment could start.
More top news
David Cameron will stand down as Conservative leader ahead of the general election expected in 2020, Iain Duncan Smith said.
Delegates at the SNP spring conference have backed a move to allow all-female shortlists in the Scottish Parliament election next year.
Michael Clarke ended his one-day international career by leading Australia to a simple World Cup final win over New Zealand.