BBC News has learned that, on average, levels of omega-3s halved in the fish over that period. Despite this, the analysis shows that farmed salmon is still one of the richest sources of these fatty acids.
But the industry is exploring new ways to arrest the decline - which appears to be due to the type of feed given to the farmed fish.
The study was carried out by researchers at Stirling University. Prof Douglas Tocher, who led the research, told BBC News: "About five years ago, a portion of Atlantic salmon of 130g was able to deliver three-and-a-half grams of beneficial omega-3. This is actually our weekly recommended intake. Now, the level of omega-3 has halved," he said.
"Therefore, instead of eating one portion of farmed salmon, we would need to eat two portions of farmed salmon," he explained.
Omega-3 fatty acids play vital roles in many fundamental processes in the body.
Prof Tocher stressed that farmed salmon was still one of the richest sources of beneficial fish oils and he urged people who buy farmed salmon for its potential health benefits to continue doing so.
"Farmed salmon is just about the best way of getting omega-3 in our diet. All the other fish are much lower than mid-Atlantic salmon, including wild salmon," he said.
But Prof Tocher told BBC News that he was concerned about what could happen to omega-3 levels in a few years' time.
"If nothing was done, the level of the beneficial omega-3 can only really go down," he explained.
Prof Tocher's colleague Dr Matthew Sprague said that the government should consider changing its advice to consumers.
"At the moment, they are advising to eat two portions of fish per week - one of which should be oily. But the advice of one portion of oily fish really should now be two portions at least," he said.
In response to the results Dr Alison Tedstone, chief nutritionist at Public Health England, said: "ultimately we all need to eat more oily fish; on average adults only consume 54g of oily fish per week when official advice is to eat at least 140. Our independent experts keep abreast of the evidence base to ensure advice remains up to date."
Omega-3 levels in farmed salmon have dropped because of the industry's success.
The farmed salmon get their omega-3s from smaller oily fish such as anchovies, which have been ground up and added to their feed.
The more oily fish that goes into the feed, the more omega-3 the salmon contains. Not long ago, 80% of the feed was made up from oily fish. Now, it's more like 20%.
The decline is a result of the industry having to cut back on the amount of anchovies it uses in feed because, previously, it was recognised that far too many anchovies were being caught for fish food.
There has also been a growing demand for farmed salmon across the world. According to Dr Paul Morris, of Marine Harvest, one of the world's largest producers of farmed salmon, a much reduced supply of fish oil for feed has had to be spread ever thinner.
"We have a fixed amount of fish oil, and we are making sure that we are using that as efficiently as possible. That won't get us further than a certain amount of the way, so ultimately we will have to look at other sources of (beneficial) omega-3," he said.
Farmed salmon have had very high levels of omega-3 in the past because of the easy availability of fish oil and fish meal. That has given the industry a breathing space in order to find a solution, according to Dr Morris.
"Farmed salmon will continue to be a really good source of omega-3 in the future even if we reduce the amount compared with today. (But it will be) five to 10 years before we really run into an issue and we need solutions on the table before then."
One solution the industry is looking at is to produce fish oils using marine algae, which is how it is produced in the sea. But it is currently uneconomic to reproduce this process in factories.
Another possibility is to grow oil seed rape plants that have been genetically modified to produce fish oils.
Prof Jonathan Napier of Rothamsted Research in Harpenden has grown these plants in the UK's only field trials of GM crops. He believes that his GM plants could provide the industry with an economic solution.
"You could grow this crop on a thousand acres, or 10,000 acres or a million acres. So, basically, the production of omega-3 fish oils is no longer limited by the amount of fish you can catch from the ocean," he said.
"It is going to be helped by what we can produce by agriculture. We think this is a great potential solution to help fish farming become more sustainable and continue to grow as an industry."
But the industry won't introduce feed produced by GM technology unless consumers accept it. They do in the US and in Asia - but not in Europe.
According to Steve Bracken, who is the business development manager for Marine Harvest, consumers in Europe will face a choice.
"You have to take a very long-term view of this because you are talking about nine billion people on the planet by 2050 so we have to be producing more from the sea," he explained.
"Agriculture is being stretched so farming from the sea is what it's all about - that's the future".