The main responsibility for the mission will be shouldered by France and Germany.
It was overwhelmingly approved by 440 votes to 135 by the Bundestag, the lower house of parliament. Six deputies abstained.
The four-month mission has been met with suspicion in both the DRC and Germany, which has a post-war tradition of extreme caution on sending troops abroad.
But it won parliamentary approval through the backing of the two parties in Chancellor Angela Merkel's ruling coalition, the Social Democrats and the Christian Democrats, as well as the Greens.
"This is not Iraq. It is a chance to make a contribution to efforts to rebuild the DRC through a relatively small investment," said Christoph Straesser from the Social Democrats.
The opposition liberal Free Democrats and the neo-communist Left Party opposed the mission, arguing that the Germans risked becoming embroiled in a bitter conflict on unfamiliar territory if the July 30 vote descends into violence.
Ms Merkel has insisted the peacekeeping force was "vital" as there can be no stability in Africa without peace in the war-torn DRC.
Troops based in Gabon
The mission will mark the first time that Germany has sent troops to Africa since it contributed men to a United Nations relief operation in Somalia in 1993.
Germany will host the overall command centre for the planned 2,000-strong EU force in Potsdam, outside Berlin, while French soldiers will run an operations centre in the DRC capital Kinshasa. France will contribute 850 men to the mission.
Most of the EU soldiers will be based outside the DRC, acting as a rapid reaction force ready to intervene at the request of the United Nations if violence erupts, notably to help evacuate foreigners.
About 1,000 troops will be based in Gabon’s capital Libreville, to the west of the DRC.
French soldiers who are permanently stationed in Gabon will be joined by another 450 European soldiers, mainly Germans.
Another 200 will be based in Port-Gentil, 200 kilometres south of Libreville.
Their help was requested by the United Nations' mission in the DRC, known as MONUC.
The mission wanted help in evacuating Europeans if needed and to send a strong message that the international community backed the first elections since the DRC gained independence from Belgium in 1961.