The Sam Wanamaker Theatre, named after the founder of the Globe, will seat 340 and will rely entirely on candlelight for illumination.
The £7.5m project is based on drawings, held by Worcester College, Oxford, which are believed to be the earliest surviving examples of what a Jacobean indoor theatre may have looked like.
The design, which is being delivered by architect Allies & Morrison and historic timber frame specialist Peter McCurdy & Co, includes two tiers of balcony seating and a pit with a capacity of 60 in front of a raised stage.
The McCurdy workshop team has been working on the prefabrication of the timber structure since September. Onsite erection will begin in March.
Master craftsman Peter McCurdy said the new theatre was much smaller than the Globe and would have a different look.
"The feel will come very much from the detail and craftsmanship of the timber interior," said Mr McCurdy.
