The issue had been a major bone of contention during the Brexit talks, reports Xinhua news agency.
Among others, the agreement sets out the total of allowable catches (TACs) for 75 shared fish stocks and a number of deep-sea stocks.
It also clarifies access limits for species that are not covered by a quota.
"The agreement guarantees stability for fishermen and women in both the UK and the EU, while also ensuring sustainable management of marine resources," the Council said in a statement following the approval on Friday.
It added that the agreement is also in line with the social, environmental and economic principles of the bloc's Common Fisheries Policy, provides the certainty needed by the fishing industry, and paves the way for future consultations with the UK on fishing rights.
The agreement was reached after several rounds of negotiations.
Under the terms of the EU-UK Trade and Cooperation Agreement concluded in December 2020, the two sides agreed to hold annual consultations on fishing opportunities.
Following the Council's approval, the agreement will now be transposed into EU legislation.
A specialised committee on fisheries will also be set up to finalise some of the pending issues, including quota swaps and certain technical measures.