Graham Construction fitted the final pane of glass to the new structure in November.
A topping out ceremony was held to mark the occasion.
The works are part of a 'major' redevelopment at the research university.
The 'SOAS into Senate House' project will extend SOAS's central-London campus.
Work will now begin to fit out the 1,000 sq m space below the glass roof to form a social learning platform and café.
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Meanwhile, refurbishment of the original Grade II listed building is continuing, with restored historic features concealing new electrical, data and heating systems.
The sustainable glass roof will help keep running costs and energy consumption to a minimum, while rainfall will be collected from the structure and transported to the rainwater harvester for use in flushing the building's toilets.
GRAHAM Construction's London Office Director Rob Joyce said: "This topping out ceremony marks an important milestone. We are now one step closer to completing a state-of the-art building which will be a great resource for the university and one which better meets their needs and further enhances the student experience. Our team are working hard to push through to completion so that students can start making the most of the new facilities."
(LM/MH)
