The 1,800 foreign personnel, plus around 1,000 local staff, will make up the EULEX Kosovo mission.
The EU police and customs officers, prosecutors, and judges, which will begin deploying to the region next week, are to help build institutions for Kosovo that are free of political interference.
The mission will be able to intervene in sensitive areas such as fighting corruption and organized crime and arresting war crimes suspects.
EULEX is to be put in place over the next four months, and is expected to take over from the United Nations by early June. The UN has administered Kosovo since a NATO bombing campaign in 1999 drove out Serbian forces.
The decision was formalized by a so-called "silent procedure," under which members of the 27-nation bloc had until midnight on February 15 to voice objections.
Speaking after a meeting with religious leaders in Kosovo's capital, Pristina, Prime Minister Hashim Thaci suggested that the province will declare independence from Serbia on February 17.
"Tomorrow will be a day of calm, of understanding and of state engagements for the implementation of the will of the citizens of Kosovo," he said. "The Belgrade authorities cannot influence the flow of processes in Kosovo."
Meanwhile, Lieutenant General Xavier Bout de Marnhac, commander of NATO's peacekeeping force in Kosovo (KFOR), said peacekeepers would not tolerate any unrest in the region.
"KFOR is almost fully deployed and we will still increase our level of activities for the next couple of days," he said. "I just want to state very strongly that KFOR will react and will oppose any kind of provocation that may happen during these days wherever they come from -- either from the Albanian or Serbian side."
Meanwhile, Serbia's pro-Western President Boris Tadic pledged to continue fighting for Kosovo to remain in Serbia.
"I swear that I will invest all my efforts in the preservation of the sovereignty and the integrity of the territory of the Republic of Serbia, including Kosovo and Metohija as its integral part, and I will also protect human and minority rights and freedoms," he said in parliament in Belgrade on February 15 as he took the oath of office after winning reelection.
The United States and most EU members say they will support Kosovo's independence, but Serbia and Russia fiercely oppose the move.
Belgrade has threatened to use diplomatic and economic measures against Kosovo, though it has ruled out using force. The Serbian government adopted a resolution on February 15 calling any unilateral act by Kosovo's ethnic-Albanian leadership to declare independence invalid and illegal.
Speaking on February 15 at a ceremony in Orasac to mark national statehood day, Serbian Prime Minister Vojislav Kostunica said the resolution preemptively annuls the creation of a state in Kosovo.
"All statehood institutions and citizens should stay united in defending Kosovo," he said. "That is the only issue in which we should not be divided on. The government of Serbia yesterday made a historic decision to annul, preemptively and forever, the creation of the false state of Kosovo."
Speaking to reporters the same day in Pristina, Kosovar Prime Minister Thaci sought to reassure the province's Serbian minority that it would not face discrimination.
"In independent Kosovo, none of the citizens will be discriminated against or left aside. I will be strongly engaged in the protection of citizens, as well as the Kosovo government under local institutions, to ensure that issues concerning minorities are protected by our constitution," Thaci said.
EU foreign-policy chief Javier Solana said the EULEX mission will be headed by retired French Lieutenant General Yves de Kermabon, who was the commander of NATO's KFOR mission in the province in 2004 and 2005.
Veteran Dutch diplomat Pieter Feith will act as the EU special representative in Kosovo.
Germany, Italy, France, and Britain are to be the main contributors to EULEX, which will also involve personnel from non-EU countries Croatia, Norway, Turkey, Switzerland, and the United States.
An ethnic Serb silhouetted against his home in the ethnically divided town of Caglavica. (Photo by Valentinas Mite)
In December, RFE/RL correspondent Valentinas Mite traveled to Kosovo, where he photographed the everyday realities that underlie the emotionally charged debate surrounding the region's ethnic divisions.
Click here for a slideshow of images from Kosovo.