The girl, named Elsa, was discovered by a person walking their dog one night in January near a busy junction in the Newham district, police said.
Subsequent DNA tests revealed that Elsa was the full sibling of two other babies who had also been abandoned in the same area.
Harry, the first baby, was found in a park in Newham in September 2017, and in January 2019 another baby, named Roman, was discovered by dog walkers at a children's play area.
Details of the case were made public on Tuesday after a judge at a family court in east London said the story was of public interest and gave the BBC and PA Media permission to report the sibling link of the three abandoned children.
The BBC said the older children had since been adopted while Elsa, who was estimated to have been born only an hour before being abandoned, was in foster care.
The court was told she was doing well, according to the BBC.
"We understand the significant public interest that will come following the lifting of restrictions that allow this information to be reported," Detective Inspector Jamie Humm said in a statement.
"It is significant news and our work has focused on trying to locate the mother and provide support to her."
The BBC said the family court was told the children will all know they are siblings and there were plans for them to have some form of contact as they grew up.
