The Scottish Government called the deal between EU fishing ministers in Brussels an important milestone to end "the 30-year scandal of discards".
The UK Government hailed "a historic victory in Brussels".
Discards of fish which are not the correct species are estimated to represent around 25% of total catches under the present European quota systems.
Ending them is seen as a vital step to conserving threatened stocks such as mackerel, herring, cod, haddock, plaice and sole.
The Scottish fleet has been making great efforts to reduce discards, using different nets.
Bertie Armstrong, chief executive of the Scottish Fishermen's Federation said it was a practical plan that would work for the fishing industry. "We also welcome the provision for a degree of flexibility in the plan so as to take into account any practical difficulties in implementing the scheme," he said.
Scotland's Fisheries Minister Richard Lochhead said: "No longer will European fishermen be dumping millions of tons of fish overboard which is a waste of a valuable food resource to the detriment of our stocks and the industry."