The farms were originally owned by Morpol, which had Polish roots, but the sale was demanded to avoid Marine Harvest controlling some 40% of the Scottish salmon industry.
Norwegian-headquartered Marine Harvest retains extensive fish farm interests in the west of Scotland employing nearly 370 people. It also has a head office for Scotland based in Edinburgh.
Marine Harvest, the world's biggest fish farmer, expects to book a gain of 300 million crowns (£30.1m) on the deal and said the sale would increase its potential dividend pay-out.
The operations in Orkney and Shetland are expected to harvest 17.4 thousand tonnes of fish this year.
The deal is expected to close in the second quarter of this year.
It is conditional on the European Commission agreeing that the purchaser, the transaction and the sales terms meet remedies set out in September when Marine Harvest took control of Morpol.
Cooke chief executive Glenn Cooke said: "We are always looking for strategic development and investment opportunities in the seafood sector.
"This purchase gives us a unique platform for our European operations and is a good fit with our Spanish sea bass and sea bream farming company, Culmarex. We will be able to leverage our global relationships with suppliers and build on Meridian's excellent market reach into both the European and US marketplace.
"We believe this investment in the well respected Scottish industry creates value for our entire group and strengthens our European foothold."
Marine Harvest retains interests in the Northern Isles after spending £65m on acquiring a quarter of the shares in fellow Norwegian-based firm Grieg Seafood in November.
Marine Harvest said last month that 2013 was its best year so far, with all time high revenues and operating profit.
This included record profit for its Scottish operations where Marine Harvest has 25 sea farms around Lewis, Harris, the Uists, Skye, Wester Ross and Lochaber.
It also has four freshwater sites, five hatcheries, and a harvest station at Mallaig.