The bridge - which sweeps across the lush Arstaviken bay - is a significant development in the modernisation of Sweden's railway.
The red pigment of the concrete was specified to resonate with the 'Falu-red' timber used in Stockholm's traditional buildings.
Following an international competition in 1994, Foster and Partners, together with Ove Arup, were selected to design the new bridge, which incorporates two new train tracks, a pedestrian and cycle way, and a maintenance access road.
Speaking at the inauguration, which was attended by King Carl XVI Gustaf, Foster said: 'Our design for the new Arsta bridge is driven by the desire to celebrate the visual impact of the Arstaviken bay on entering Stockholm.
'We have tried to respond sensitively to the surrounding landscape by creating a bridge that merges seamlessly with its context,' he added.