The aircraft, ordered by four European countries that are involved in its development, is ready for the next stage of assembly, the company said.
"Over the next few months, the fin and foreplanes will be fitted and all the systems will be married-up," BAE Systems said. "Tranche 3 capability represents the next significant milestone in the evolution of this remarkable combat aircraft.
The Typhoon is a twin-engine, canard-delta wing, multirole fighter designed by EADS, Alenia Aeronautica and BAE Systems, working through the Eurofighter GmbH holding company. Its maximum speed at altitude is more than 1,500 miles per hour. Its maximum ceiling is about 55,000 feet.
It is in service with the air forces of Australia, Italy, Germany, Britain and Saudi Arabia.
A total of 112 Tranche 2 Typhoons have been ordered for the four European partner nations, with deliveries expected to begin next year.