Now the plan goes to EU presidents and prime ministers, who are scheduled to meet in Brussels, Belgium, on Wednesday to consider it.
In the interior ministers' vote, four countries -- Romania, the Czech Republic, Slovakia and Hungary -- opposed quotas, but they will be obligated to take in asylum-seekers, the source said. Finland abstained.
Eastern European countries in particular have shown resistance to committing to quotas, as reflected in those countries that voted against the idea at Tuesday's meeting in Brussels.
They'll have to comply with the resettlement plan even if they voted against it, the EU source said.
"The mechanisms of resettlement are obligatory," the source said.
Wave of migrants in Croatia
The Balkan nation of Croatia grappled with an increasing wave of migrants on Tuesday.
Croatian officials said that 2,400 migrants had entered the country in just the past 12 hours. Nearly 35,000 people have already arrived in the country, which has a population of only 4.4 million.
Europe as a whole has struggled in recent weeks to fashion a coherent response to a historic wave of people fleeing conflict and destruction in the Middle East and North Africa -- primarily from Syria, where a civil war has raged for more than four years, leaving cities in ruins.
So far, 34,900 migrants have been allowed into Croatia, the Ministry of Interior said in a statement. But the migrants are moving through the country to other destinations fairly efficiently, Croatia said, with 5,100 transported out of the country on Monday and a further 1,160 by Tuesday morning.
Currently 1,630 people are at a camp in Opatovac, in eastern Croatia near the border with Serbia, where video feeds showed them waiting for transportation and lined up for aid.
German official: Islamists may recruit among migrants
The historic migration has fueled fears that the population of Europe -- and the culture of the continent -- will be changed beyond recognition. It is a prospect some in Europe fear.
On Tuesday, Germany's top domestic security chief said that hardline Islamists in the country might recruit supporters among new refugees and migrants -- though many of those migrants are, in fact, fleeing hardline Islamists in the form of the terrorist group ISIS.
"We are watching Salafists appear as benefactors and helpers to contact refugees directly with the aim of inviting them into mosques," Hans-Georg Maassen, head of the Federal Office of Protection of the Constitution, said in an interview published in the Rheinische Post. Salafists are ultraconservative Muslims.
"They want to recruit refugees for their affairs," Maassen said.
More than 430,000 migrants have come to Europe by sea so far this year, double the number that arrived during all of 2014, according to the International Organization for Migration.