The new bridge, a graceful line with an arch stretching across it, will bear the E6 motorway between the two countries. The total length is 704 metres with a bridge span of 247 metres. The maximum height is 92 metres.
The total cost of the project is around 675 million kronor but the bridge, with its four traffic lanes, will simplify cross-border trade in the south of the two countries.
Norwegians travel often to Sweden to stock up on meat and alcohol, which are up to half the price across the border.
The two royal families, each arriving from their side, met up at the middle of the bridge where they unveiled two granite sculptures of a pair of hands reaching out to one another.
“I can hardly imagine a more symbolic way to mark the excellent relations between our two countries,” the Norwegian monarch said in an address.
“These are two powerful hands reaching out to the future,” the Swedish king said.
The inauguration is one of the highlights scheduled for the 100th anniversary of Norway’s independence.
Norway and Sweden were joined in a political union until 1905, when the Norwegian parliament unilaterally cancelled it after failing to obtain its own diplomatic corps.