Last year, National Grid said it would use underground cables instead of pylons between Anglesey and the mainland in Gwynedd.
It said this would protect the Menai Strait's natural beauty.
The tunnel will be based on a network of power tunnels in central London.
Plans to connect Wylfa Newydd at Cemaes Bay to a substation at Pentir, Gwynedd, have been controversial, with campaigners concerned about the impact of pylons.
Aled Rowlands, external affairs manager for National Grid, said: "We are going to be using the same type of technology [that we are using under the River Thames] to go underneath the Menai.
"When we've listened to local people and to those specialist bodies, they've asked us to preserve the natural beauty that's already there.
"This option is more expensive than just putting cables across the top, but we think it's worth it.
"We are looking at probably over £100m just for this cable tunnel to take the link from Anglesey over to the mainland and into the National Grid.
"Here in London, we are digging through London clay. There are very different conditions around the Menai, with some rock and some limestone and some other things, so it's going to be a real engineering challenge for us.
"But at National Grid we do have an expertise in that.
"This project for 34km [in London] has taken about eight years. We think it will be... four or five to build those 4km from Anglesey across to Gwynedd."
Plaid Cymru MP for Arfon Hywel Williams and AM Sian Gwenllian have met with National Grid bosses to push for undergrounding the remaining 1km of electricity connection, for which pylons are currently proposed.
The National Grid has published an interactive map showing the proposed routes of the power cables.
A tunnel under the Menai Strait, which will contain cables linking Wylfa Newydd nuclear power station to the National Grid, is set to cost £100m and take up to five years to complete.