On Thursday the FSA revealed the results of tests on the products, which are made by French supplier Comigel.
Of 18 beef lasagnes tested, 11 contained from 60 to 100% horsemeat, they said.
Supermarkets Tesco and Aldi have already removed a range of ready meals made by the French supplier and Findus recalled the lasagnes as a precautionary measure earlier this week.
The FSA said there was no evidence to prove the food is a safety risk.
An FSA statement said: "As part of its ongoing investigation into mislabelled meat, the Food Standards Agency has confirmed that the meat content of beef lasagne products recalled by Findus has tested positive for more than 60% horse meat.
"Findus withdrew the beef lasagne products after its French supplier, Comigel, raised concerns about the type of meat used in the lasagne.
"We have no evidence to suggest that this is a food safety risk. However, the FSA has ordered Findus to test the lasagne for the veterinary drug phenylbutazone, or 'bute'. Animals treated with phenylbutazone are not allowed to enter the food chain as it may pose a risk to human health."
Findus UK have apologised to any customers affected and urged them to contact their customer careline for a refund.
"We understand this it is a very sensitive subject for consumers and we would like to reassure you we have reacted immediately," a spokesperson said.
We are confident that we have fully resolved this supply chain issue. Fully compliant beef lasagne will be in stores again soon.
A number of Irish companies are embroiled in the meat scandal.
On Wednesday supermarket chain Asda withdrew four frozen burger products supplied by Northern Irish company Freeza Meats.
A consignment of meat being held in quarantine by the company was tested and found to contain 80% horsemeat on Monday.
The Newry firm said it had been storing the meat, which was from Poland, in its cold store as a goodwill gesture after refusing to buy it from trader McAdam Foods, based in the Republic and the meat never entered the local food chain.
Asda said that while no horse DNA has been found in burgers supplied by Freeza, it has taken them off the shelves as a precaution.
Director of the family-run business Freeza Meats, Paul Mackle told UTV he was shocked and angry about the situation, which he believes could force them to shut.
Newry and Mourne District Council's Environmental Health Department confirmed the suspect meat consignment had been detained for the last five months "due to the condition of its wrapping and queries regarding its labelling and traceability".
On Tuesday John Farrell, the council's Director of Environment, Health & Building Services, said Freeza Meats was put in a difficult position "through no fault of their own".
Meanwhile McAdams Foods, based in Co Monaghan, said it was shocked to find horsemeat in the meat product it imported and was cooperating fully with authorities.
It has also emerged that the Bureau of Criminal Investigation is assisting the inquiry team into the horsemeat scandal, after the Food Safety Authority said they believed there was an element of fraud surrounding the contaminated beef products.
Polish officials had written to Ireland requesting proof that the contaminated produce is linked to Poland as they claimed they have have found no evidence of horse DNA and said there is no evidence of falsified labels.