The emergency proposal, which comes atop another one to resettle in member states some 20,000 Syrian refugees, is in response to a surge in migrants making the dangerous crossing over the Mediterranean.
Both Rome and Athens, which are struggling with the wave of migrants, appealed to the 26 other EU states to share the burden.
Italy's refugee-reception facilities are stretched to breaking point with 80,000 people currently being housed in them and local authorities are growing increasingly impatient with the demands placed upon them.
"Syrians and Eritreans will be relocated from Italy and Greece to other European Union member states over a period of two years," he said.
The measure concerns people arriving in those countries after April 15 this year, the commissioner said.
The proposal suggests migrants be distributed according to four criteria: gross national product, population, unemployment and the number of asylum requests already registered in the country.
The commission said member states will be given 6,000 euros (about USD 6,500) per asylum seeker.
Under the plan, a country like France would resettle 2,375 Syrian refugees.
However, EU states Britain, Ireland and Denmark can opt out of both the relocation and resettlement schemes under existing EU treaties, according to EU officials.
Avramopoulos insisted that the European Commission, the executive arm of the 28-nation EU, was not proposing a quota system for distributing people.
Many member states, which are under pressure from anti-immigrant parties during tough economic times, have strongly objected to quotas.