Ministers have agreed to ban discards of mackerel and herring before 2014.
A phased ban on discards of cod, haddock, plaice and sole will be implemented before 2018.
They also agreed that EU regions should be given more control over fisheries policy.
A major step
The Department for Environment, Food and Rural Affairs hailed the agreement as “a major step towards radical reform of the broken Common Fisheries Policy [CFP]”.
Richard Benyon, minister for the natural environment and fisheries, said:“After years of pressing to eliminate discards it was always my aim to get the Council to agree to end this wasteful practice as soon as possible.
“While I am disappointed that the Council has not agreed the firm dates that I was seeking, a commitment to eliminating discards is a step in the right direction.”
Benyon added: “For far too long overly detailed decisions have been taken from Brussels and fishermen throughout Europe have been micro-managed. The agreement we reached today will hopefully see some of that power return back to Member States, working with their fishermen.”
A statement from the seafood authority Seafish welcomed the agreement but highlighted two key challenges. "First, no matter what timescale is eventually agreed for phasing out discards, we must do more to quantify the level of discards for both commercial and non-commercial species,” it said.
“Second, we do need a more systematic study of the survival rates of various species both post-escape (from the fishing gear) and post capture (discarded from the vessel). Without a better evidence base, it will not be possible to implement the provision that allows discarding where survival rates are high.”
Speaking before the agreement, Fearnley-Whittingstall told BBC Radio4'sToday prgramme: “We want to see a discards ban. Half a million tonnes of fish – including prime cod – are thrown away every year because fishermen are over quota.”
Thrown away
Sometimes smaller fish are thrown away by fishermen anxious to reserve their quota for bigger fish, he added.
Fearnley-Whittingstall said: "This is a key meeting – lines will be drawn that will be very hard to retract or adapt afterwards.”
The TV chef has led a high-profile campaign to ban fish discards based on his series for Channel 4 TV's Fish Fight. More than 650,000 people have signed a petition supporting an end to discards.
Celebrity supporters include: Stephen Fry, Ricky Gervais, Jamie Oliver and Jeremy Paxman.
Commenting on discards, Paxman said: “If this is conservation, then I’m the Mad Hatter.”
It is thought unlikely that the proposed discard ban will be finally agreed by the EU Parliament and Commission before the end of the year.