Horizon Nuclear Power described it as a milestone in the process of building the reactors at Wylfa on Anglesey.
The Office for Nuclear Regulation (ONR) will spend 19 months assessing the suitability of the site, the organisation and the reactor designs.
Horizon Nuclear said it now hopes to have all permissions in place for 2018.
The nuclear firm - owned by Hitachi Ltd - said on Tuesday its focus would now be on providing the ONR with "confidence in our ability to safely deliver this crucial project".
"Today's announcement marks a significant development in the maturity and growth of Horizon as we get ready to build and operate our lead site at Wylfa Newydd," said Anthony Webb, its safety and licensing director.
"We already have a proven technology, aligned with experienced leadership, and we are rapidly building the wider capability and organisation to help ensure success."
The site licence application is one of several key consents needed before the Â£8bn project can proceed.
Horizon is already preparing for a final public consultation in the summer before submitting a Development Consent Order request to the UK Government's Planning Inspectorate.
At the same time, the advance boiling water reactors it wants to use in the new power plant are undergoing the fourth and final stage of a Generic Design Assessment to ensure the technology is safe and works. The process is expected to finish at the end of 2017.
"This is the first licence application for a new nuclear power station since 2011, and over the past three years we have been engaged with Horizon, providing them advice on the licensing process and the robust requirements expected of a nuclear site licensee," said Mike Finnerty, deputy chief inspector for the ONR.
If all the planning and safety regulations are approved, concrete could start flowing on the new site next to the former Wylfa power plant by 2020.
A bid to build a new nuclear power plant in north Wales has taken a major step forward with an official application for a site licence.