The two companies said they had completed a feasibility study and have submitted a "scoping report" outlining their intentions to the Department of Business, Enterprise and Regulatory Reform.
They are now required to produce detailed environmental impact assessments to accompany a future planning application.
If approved, the companies say the plant could be operational within three to four years.
Amaan Lafayette of Eon UK said: "The waters off the coast of Wales have some of the greatest potential for marine-generated energy in Europe.
"This project will help us to harness the power of the tides and turn that potential into the clean, renewable energy we need to help fight the effects of climate change.
"If it gets the go-ahead, this scheme will be one of the largest tidal stream projects of its kind in the world."
Gordon James, director of Friends of the Earth Cymru, said: "We have to tap into marine sources to generate energy that does not emit large amounts of CO2.
"Of course they will have to ensure that the environmental safeguards are met.
"In principle I hope that it does over come any potential obstacles."
He said "the crisis of climate change" meant many more wind and wave power plants were need to replace fossil fuels "and as quickly as possible."