The NOK1.6bn (£180m) tunnel will be about 36m wide and 1.7km long, running through solid rock.
It would bypass the Stad peninsula in Selje, which is a very exposed area of the coast.
The Norwegian government said that the tunnel will reduce accident risk and improve conditions for sailors along the coast. "This is a spectacular project that we are looking forward to taking on," said coastal director Kirsti Slotsvik.
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