* Europe agrees to end decades of over-fishing
* Deal aims for sharp reduction in fish discards
* EU Commission says policy must follow the science (Adds official comments, reaction from campaign groups)
By Claire Davenport and Charlie Dunmore
BRUSSELS, May 30 (Reuters) - The European Union agreed on Thursday to put an end to decades of over-fishing and rebuild dwindling stocks by 2020, as part of a deal to overhaul the bloc's fisheries policy.
The agreement will put an end to annual haggling over catch quotas by EU ministers in Brussels, widely blamed for putting short-term economic interests above the long-term health of European fish stocks.
"We have reached a deal that is hugely valuable in terms of its contribution to the future of fish stocks," Simon Coveney, the Irish minister for agriculture told a news conference on Thursday.
Officials said agreement to follow scientific recommendations more closely in setting future quotas could increase EU fish stocks by up to 15 million tonnes by the end of the decade.
"We are aligning our fishing opportunities with scientific advice," Maria Damanaki, the EU commissioner for fisheries told the news conference.
The reform also aims to massively reduce the wasteful practice known as discarding, which sees European fishermen throw almost 2 million tonnes of unwanted fish back into the sea each year - often dead or dying - as they seek to fill strict quotas with the most valuable species.
Britain, which is debating whether to remain part of the 27-nation European Union or seek looser ties with the bloc, managed to win more sovereignty for its fishermen by getting more regional management of its fish stocks.
"We are going to stop having all the decision-making take place here in Brussels," Damanaki said.
British liberal member of the European Parliament and head of its "Fish for the Future" group, Chris Davies, described the agreement as a major step to promote sustainable fishing.
"Our treatment of Europe's seas has been a disgrace. But we have learnt lessons. Across Europe there is a strong desire now to listen to the scientists, rebuild fish stocks, cut discards, and give our fishing industry a better future," he said.
The Pew Charitable Trust, which campaigned for decision-makers to follow the science to rebuild stocks, welcomed the agreement. But it said a deal was still needed on EU fishing subsidies, to help in funding the scientific research.
The World Wide Fund for Nature criticised the deal as not bold enough to replenish fish stocks. A WWF report said it would take more than 100 years for stocks to recover.
The bloc's roughly 1 billion euro-per-year ($1.30 billion) common fisheries policy has been blamed for driving decades of over-fishing, with generous subsidies leading to a massive over-capacity in the fishing fleet.
As a result, the Commission estimates that 75 percent of European fish stocks are currently over-fished, compared with 25 percent worldwide.
As part of the deal, EU fishing nations will have to reduce the size of their fleets to reflect their overall quotas, or face the loss of some subsidies.
The deal must now be rubber-stamped by EU governments and the full European Parliament before taking effect next year, but the details are unlikely to change.
Europe had the third-highest fish catches globally behind China and Indonesia in 2010, the most recent data from the U.N. Food and Agriculture Organization showed.
Europe's top fishing nations are Denmark, Spain, Britain and France, which together account for about half of all EU catches. ($1 = 0.7712 euros) (Reporting by Charlie Dunmore and Claire Davenport; editing by Lisa Shumaker and Rex Merrifield)