The 4.9acre site is located next to Battersea Power Station on Prince of Wales Drive .
National Grid’s future plan for the site – which would be subject to a separate planning application – is to build new homes, shops, offices, leisure facilities and new public spaces.
The gasholders are no longer needed to store gas and were decommissioned last year.
Demolition works are expected to begin in the spring and would take approximately 16 months to complete.
The demolition consent removes a potential barrier to regenerating neighbouring investment sites including Marco Polo House and Battersea Power Station because sites near a gasholder facility are subject to heath and safety regulations which can prohibit development.
Planning chairman Cllr Nick Cuff said: “Demolishing the gasholders will be an important step towards bringing this redundant site back into use. We hope to see hundreds of new jobs and homes created here in the years ahead.
“The facility occupies a very important position next to Battersea Power Station where a new shopping area, Tube station and riverside park are planned. Redeveloping the gasholders site could create important new routes between this emerging town centre and established Battersea communities to the south.”