The centre has been closed for 21 months while Foster radically restructured the building.
The centre has undergone major changes, including a new exhibition area, enlarged visitor reception and shop spaces, an education studio, a refurbished cafe and disabled access.
The 1978 gallery was built to house the Robert and Lisa Sainsbury Collection of world art and represented one of Foster's most important early commissions.
'The Sainsbury Centre for Visual Arts was a formative project for me in all sorts of ways - personally and professionally. Revisiting it - 'reinventing' it to some degree - more than 30 years later has been an exciting privilege,' Foster said.
'The quality of the architecture is closely bound to the enlightenment and the driving force of Robert and Lisa Sainsbury. The building challenged preconceptions about museums. It was a gallery without walls in the conventional sense. It was also an early example of low-energy, 'green' architecture.
'We have sought to create new connections between the different parts of the building, to improve amenities and to ensure that the Sainsbury Centre is equipped to meet the demands of a new century and a developing campus,' he added.
The centre will officially reopen on 21 May.