The Wolverhampton-based company received the contract in October last year and work on the bridge, which was originally erected in 1880, is scheduled to begin in January 2009.
According to the company, the entire lift took just over a week to complete.
Pontoons were used to carry beams across the River Tees with delivery restricted to one side of the bank due to constraints of a nearby railway.
The company used 800t and 500t cranes to deliver 18 beams to barges that then took them across the river.
A spokesperson for Network Rail said: ‘This project is one of the largest civil engineering projects being undertaken in the north east by Network Rail this financial year and, despite the wind causing some delays, the overall project is still on track to be completed in early June 2009 when rail passengers will be able to travel across the new bridge.
‘This project has taken careful and detailed planning and it is a testament to all involved that this key milestone has been achieved.’