Balfour Beatty will start next month on a temporary station, before demolishing of the existing one and starting work later next year.
The new two-level station will open in 2017 and will be built above two new dedicated Crossrail tracks and those used by North Kent services.
Its £130m cost includes laying a two-mile stretch of dedicated Crossrail lines from Abbey Wood to the Plumstead tunnel portal and works to modify several bridges along the route to accommodate the overhead electric wires and two new lines.
Rob McIntosh, Network Rail’s Crossrail Programme Director, said: “We’re delighted our designs have been approved and that we can now get on with the job of delivering this transformational project on behalf of Crossrail. We’ll continue working with our partners and local stakeholders to deliver a railway that is safe, efficient and fit for the 21st Century.”
From 2018, Crossrail will add up to 12 extra trains an hour, linking Abbey Wood with central London and beyond, cutting journey times and reducing congestion on existing services.