Part of the Elephant and Castle regeneration programme, the centre will offer local people a chance to gain access into the media professions and creative industries.
The derelict Victorian library is being extended and refurbished to house training facilities, a space for community groups, a café and a commercial space to generate income for the centre.
Funded by the Elephant Links Single Regeneration Budget (SRB) programme and Southwark council, the project aims to help people find employment in the area's rapidly expanding cultural industries.
Elephant Links is in the final year of a seven-year economic development and social programme, which is paving the way for the Southwark council-led £1.5 billion regeneration.
Elephant Links SRB director Martin Smith said: 'We're thrilled that construction has started on the new centre, which provides one of the first major physical improvements to the area.
'The centre, along with the arrival of the Siobhan Davies Dance Company, demonstrates Elephant and Castle's emergence as a significant cultural quarter,' he added.
The building is expected to open its doors in June next year.