A feasibility study proposed replacing ageing ferries with tunnels from Shetland's mainland to Yell and from Yell to Unst, describing them as "economically transformative".
Two more tunnels, to the islands of Whalsay and Bressay, could follow under the plans - which it is estimated could cost £1.5bn.
Council leaders say the tunnels would be cheaper than building new ferries and replacing harbours.
At a meeting in Lerwick on Tuesday, councillors approved exploring funding options.
Council chief executive Maggie Sandison said the project was not going to be easy, but she thought pursuing a funding solution was the "right thing to do".
This could come from a mixture of private investment, public subsidy and borrowing, alongside tolls to cover maintenance costs.
The council's transport chairperson, Moraig Lyall, said the report showed there were no technical barriers to building tunnels, which would be "cheaper in the long run" than ferries.
The council currently runs ferry services to nine islands, carrying around 750,000 passengers each year on 12 vessels at a cost of £23m per year.
Costs have risen sharply in the past decade, with some routes struggling to meet demand for vehicle places.
Lyall said: "The system we have that has served us well for decades is now no longer able to do that.
"It doesn't have the capacity and we're struggling with other things, like the ability to crew the system adequately.
"These barriers to giving the islands a really good service are not going to be easily overcome by replacing ferries with other ferries.
"The tunnel is the answer that we believe will help us solve these problems."
Unst is the UK's most northerly island and home to the UK's only spaceport, at Saxavord, as well as a sizeable aquaculture industry.
The feasibility study says tunnels could boost direct economic activity related to the spaceport as well as spin-off benefits such as other aerospace industrial development and tourism.
It says tunnels would improve the rocket facility's "competitiveness, efficiency and scope for growth" as well as improving access to labour for island businesses.
Boatbuilder Brydon Barclay of Fluggaboats on Unst predicted a tunnel would transform his company's prospects.
"It's absolutely essential," he said.
"At the moment, we're running with a ferry service that just isn't meeting the demand at all."
In drawing up its plans for tunnels, Shetland has taken inspiration from the neighbouring Atlantic archipelago 200 miles to the north west.
The Faroe Islands have been building tunnels since the 1960s and now have more than 20, including four which run under the sea, linking island communities.
The network includes a 7.1 mile (11.4km) tunnel which connects the island of Streymoy to two sides of a fjord on the island of Eysturoy via the world's only subsea roundabout.
The tunnel's deepest point is 187m (614ft) below the Atlantic and has halved the driving time between the capital Tórshavn and the islands' second biggest town, Klaksvik.
Last year the then prime minister of the Faroes, Aksel Johannesen, told BBC News that Shetland could boost growth, revitalise island life and encourage population growth by emulating his country's tunnel network.
"I think we have learned in the Faroe Islands that investment in infrastructure is a good investment," he said.
The Faroes, a self-governing nation in the Kingdom of Denmark, are home to some 54,000 people while Shetland has a population of around 23,000.
It's not just the Northern Isles which are considering fixed link solutions.
Earlier this year Western Isles council – Comhairle nan Eilean Siar – said it would
consider building tunnels or bridges across the Sounds of Harris and Barra.
The debate has been turbocharged by
discontent with the reliablility of the existing Caledonian MacBrayne ferry network which serves the Hebrides and the Clyde.
"Once Scotland builds its first tunnel, it will never stop," said Andy Sloan, executive vice president at engineering firm Cowi, which has been advising Shetland Islands Council on tunnels.
Cowi's tunnelling timeline has
three years for preliminary work and five years for construction.
The tunnel would be excavated from both ends and built with a sprayed concrete lining.
Sloan said the proposed project in Shetland was relatively straightforward from an engineering perspective.
"The real challenge is whether we as a nation take a short-term or long-term view," he added.
He described the mood music about delivering the tunnels as "positive".
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