The scheme was blocked last month by London mayor Ken Livingstone because it was to be built on a 3 ha greenfield site. He said allowing the school to go ahead would set a dangerous precedent.
This led to a threat of legal action by Southwark council, which said the lack of secondary school places in the borough meant it was essential to have the school.
Studio E beat three other shortlisted practices to win the project. These were Foster and Partners, Nicholas Grimshaw & Partners and Jestico + Whiles.
Studio E is working in partnership with contractor Willmott Dixon on plans for the school.
The Corporation of London spokesperson said it aimed to change the scheme to allow more public open space on the land.