The 135-million-pound ($230 million) project is one of the largest in the museum's 260-year history, Xinhua reported.
The centre has been designed by Rogers Stirk Harbour and Partners (RSHP), who had also designed the Shanghai Pudong Airport Terminal 2 in China.
In addition to the new public exhibitions gallery, the centre also provides laboratories and studios, as well as facilities to support an extensive British and international loan program.
The building consists of five pavilions, one of which is underground.
The contemporary design is intended to complement the British Museum's existing architecture, connecting to the historic building while maintaining its own identity.
The kiln-formed glass and Portland stone used on the pavilions are inspired by the materials of the existing buildings.