The European Commission estimates that almost a quarter of the fish caught by EU vessels is discarded, the highest rate in the world, because crews want to make sure that they fill their tight catch quotas with fish of the desired species or those that will get a good price.
The agreement should allow the EU to proceed with deep reforms to its discredited Common Fisheries Policy (CFP) to end decades of over-fishing and try to restore stocks to healthy levels by 2020.
After all-night negotiations in Brussels, ministers backed a timetable for phasing out discards, starting with pelagic or open-sea fish such as mackerel and herring in 2014, and extending to all EU fishing vessels by 2019.
But exemptions were agreed to allow fishermen to discard up to 9% of certain species in 2014, falling to 7% in 2019. That was the price for securing the support of reluctant southern European fishing nations such as Spain and Portugal.
Irish Farm and Fisheries Minister Simon Coveney, who chaired the talks, said the deal would allow him to begin negotiations with the European Commission and European Parliament to try by June to finalise reform of the CFP, already overwhelmingly backed in principle by the Parliament.
The CFP is widely regarded as having allowed subsidised, industrial-sized fleets to devastate fish stocks.
"I think people will see from what has been agreed this morning that we are serious as ministers and as countries about bringing about a fundamental change in how our fish stocks are managed, and the way in which our fishing fleets operate," he told reporters after the meeting.
EU Fisheries Commissioner Maria Damanaki, who has led efforts to overhaul the CFP, said it had been very hard for ministers reach a deal, because each country had its own priorities and fishing practices.
"After these discussions today, we can look forward to a better future for our fisheries. The new policy will be there very, very soon," she told a news briefing.
But conservation groups criticised ministers for failing to back a full discard ban, and urged the parliament to push for a more ambitious deal in the negotiations to finalise the reform.