The Unicorn Theatre is to move to a modern purpose-built theatre in Tooley Street in 2005.
Confirmation that the £11m plan will go ahead comes with the announcement that at least half the funding is already secured.
The Arts Council grant will be £4.5m and the Pool of London Partnership has promised £1m. Unicorn is a children's theatre company founded just over 50 years ago and until recently based in Leicester Square.
The new 350-seat theatre will be built near Potters Fields.
In addition the Unicorn building will include rehearsal space, a gallery and a cafe.