Andy Sloan, who has decades of experience in the area, said it is “unequivocally” possible to build the links.
It comes after Scotland Office minister Iain Stewart said a network of tunnels should be considered as a "viable" alternative to ferries.
He said the Faroe Islands – where the world's first undersea roundabout opened in 2020 – show what can be done.
The minister suggested connecting islands over shorter distances, such as within Shetland.
Mr Sloan, the managing director of engineering consultancy Cowi UK, said: "It's certainly not pie in the sky.
"I've been working on the concept of fixed links between Scottish islands for 15 years."
He added: "From a technical perspective, building these tunnels is relatively straightforward.
"So I'm keen, from my perspective, to push the debate beyond that of simply engineering.
"From an engineering perspective, we can deliver the tunnels.
"It's up to...politicians and particularly local communities to determine whether they want them or not.
"That's where the debate should be taken, I think."
Mr Sloan, who is chair of the joint venture working on the proposed Lower Thames Crossing, was previously involved in plans for a tunnel to Bressay in Shetland.
He said there is political and local support in Shetland, with a link between Unst and Yell also "eminently feasible".
He added: "I think, from a perspective of delivery, one of these shorter tunnels - Bressay, Yell, Unst in Shetland - is feasible, possibly some of the ones on the Western Isles.”
The engineer said there are "people with the skills and experience" in Scotland and the wider UK to design and deliver tunnels.
These could be built fairly quickly, he said, at a pace of up to eight or nine metres a day.
Mr Stewart previously said the tunnels in the Faroe Islands cost around £20 million per kilometre.
Mr Sloan estimated the cost in Scotland would be “somewhere north” of this, adding: "It's a big capital cost, but it's highly sustainable because they are there forever."
He said benefits in the Faroes had included a boost to average earnings and more younger people moving to island communities.
The most recently completed tunnel in the Faroes cut the travel time between Torshavn, the capital, and the village of Runavik from an hour and 14 minutes to just 16 minutes.
Mr Sloan said tunnels could also be environmentally friendly in the longer term.
He added: "There needs to be a real, open dialogue with communities to see whether they want these."
He said the conversation is currently "loudest" in Shetland, adding: "The will to have these comes from the locals, but they will not be able to deliver them in isolation.
"They need support from Holyrood and also from, I strongly suspect, Westminster."
The Scottish Government has proposed exploring the construction of fixed links in the Western Isles and between Mull and the mainland.
However, it was dismissive of Mr Stewart’s involvement, insisting transport is “a devolved matter”.