The building will cement a restructuring of the department, masterminded by new head Marcial Echenique following a turbulent couple of years suffered by the school.
The new plans are designed to enable the research unit of the department, the Martin Centre, to be moved to the main faculty premises at Scroope Terrace.
The undergraduate students, who are presently located in this building, will be moving to a new extension in the rear garden to provide a large single studio for the undergraduates and their own model-making workshop.
Scroope Terrace comprises a short, symmetrical row of 1839 Grade II-listed houses, with a 1958 Sandy Wilson extension.
Echenique said he was delighted to have won planning permission following the last 24 months, when at times it looked highly likely that the school of architecture would be closed.
He said: 'The department of architecture is the best teaching department in the UK. With our new research strategy, we will become an international leader in sustainable design, addressing one of the world's most pressing challenges.
'The department's new building will be an exemplary sustainable building, with design input from services engineers, structural engineers and architects with expertise in this field, who also teach at the university.
'The much needed refurbishment and alterations to Scroope Terrace will do much to improve the interior and enhance the teaching and learning experience in the existing studios,' Echenique added.