The 4MW scheme is being developed by Scottish firm Orbital Marine Power, which has created the world's most powerful tidal turbine - the O2.
The first of the two turbines is expected to be connected to the grid by the end of this year, with a view to being fully operational in early 2021.
When up and running, the pioneering floating devices are predicted to generate enough electricity to power up to 3,400 homes - around a third of Orkney’s needs.
The turbines are being installed at the European Marine Energy Centre (EMEC) in Orkney, a world-leading test and research facility focusing on wave and tidal power development.
The scheme will be deployed at the Fall of Warness test site, off Orkney’s northern island of Eday.
The latest move comes following successful tests of the O2 prototype, which was able to produce record levels of tidal energy - more than 3GWh - in its first year of operation.
Neil Kermode, managing director at EMEC, said: “This is fantastic news for the tidal energy industry, which has been going from strength to strength over the last three years as more gigawatt hours have been fed into the grid than ever before.
“The first floating tidal energy farm marks another step forward for the sector, which is demonstrating that it will be a vital part of the world’s drive towards net-zero.”
Andrew Scott, Orbital Marine Power chief executive, said: “We are delighted to have secured this second berth - it’s a vital step towards delivery of our first tidal array.
“The current O2 build is progressing in line with expectations, thanks to a fantastic supply chain we have working with us, and this second berth provides us the opportunity to set the vision for how we are going to further the commercialisation of our industry-leading technology and accelerate the deployment of tidal energy at scale globally.”
The plans have been welcomed by the country’s green energy industry body.
Ben Miller, senior policy manager at Scottish Renewables, said: “Scotland leads the world in the development and deployment of tidal energy technologies, and Orbital are very much at the forefront of the race to fully commercialise tidal stream turbines.
“This new development, which comes after Orbital's SR2000 machine broke world records for tidal power generation in 2019, is a great sign and clearly shows that the company is making great strides towards tapping an enormous potential global market for tidal power.”