Sixteen countries have so far offered places to meet the European Commission's goal announced in September of taking at least 50,000 refugees over the next two years under the bloc's resettlement programme.
The scheme is aimed at discouraging migrant boats from making the risky Mediterranean crossing, which is still causing deaths more than two years after the migration crisis first hit the continent in 2015.
"We are exiting crisis mode gradually and we are now managing migration in a spirit of partnership and shared responsibility, inside and outside the EU," EU migration commissioner Dimitris Avramopoulos said.
Brussels meanwhile said its controversial migrant quotas - under which member states were required to share the burden of frontline EU states - was wrapping up with just 750 people left in Greece and 3,100 in Italy left to relocate.
More From This Section
The scheme relocated 31,000 out of an originally planned total of 160,000.
The EU has launched a string of schemes to tackle the biggest influx of refugees and migrants since World War II, caused initially by people fleeing the conflict in Syria, but now mainly down to economic migrants from Africa.
"The suffering of migrants detained in Libya is an outrage to the conscience of humanity," the UN human rights chief Zeid Ra'ad Al Hussein said in a statement, adding that the policy was "inhuman.