The 17-year-old, a British national who cannot be named for legal reasons, admitted arson not endangering life at Westminster Magistrates’ Court on Tuesday.
It follows an investigation by Counter Terrorism Policing London into the attack on Saturday in Harrow.
District Judge Nina Tempia freed the teenage boy on bail with conditions, including to live and sleep at his home address in Brent and to not enter any synagogue.
She told the defendant: “I’m going to grant you bail so that you can be released today. If you breach these bail conditions you will be arrested by the police.”
The boy is due to appear at Willesden Youth Court on 4 June.
The charge comes after a 19-year-old man and a 17-year-old boy were arrested at separate addresses late on Sunday 19 April.
Both were arrested on suspicion of arson reckless as to whether life was endangered and were taken to a London police station.
The 19-year-old man has been bailed pending further enquiries.
Police said the charge relates to an alleged arson attack at around 11.35pm on Saturday at Kenton United Synagogue in Shaftsbury Avenue, Harrow.
At around midnight, officers from the Met Police who were conducting security checks at local synagogues came across what they identified as a crime scene and alerted the London Fire Brigade.
The force said that while minor damage was caused, no one was injured.
A number of Jewish sites have been targeted in separate incidents across London in recent weeks.
The Met Police have been investigating alleged attacks, which have not been linked, at the former site of a Jewish charity in Hendon on Friday, and a synagogue in Finchley on Wednesday.
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Both those incidents are near Golders Green, where four Jewish community ambulances operated by volunteer-led service Hatzola were torched in an alleged arson attack last month.
Meanwhile, on Saturday, a security incident was triggered near the Israeli embassy in central London after jars of powder, later identified as harmless, were discovered in a park.
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