Qeku had been nominated by the Alliance for Kosovo's Future, a partner of the Democratic Alliance of Kosovo (DSK) in the ruling coalition.
"The time of hatred, discrimination and the suffering of Kosovo citizens should be over. Time has come for inter-ethnic confidence, integration and general progress," the new premier said at an extraordinary session which the parliament convened today to elect Kosovo's new leadership.
Earlier in the day the parliament elected Kole Berisha its new chairman.
Qeku called on local Albanians to commit themselves to helping minorities exercise their rights in the interests of the majority ethnic group.
Addressing Serb representatives in the Serbian language, Qeku told them that "Kosovo belongs to all of us," and called on the Serbs to take part in Kosovo institutions.
"We will together organise a society which will guarantee freedom, equality and economic progress to everybody, regardless of their ethnic origin," said Qeku, whose nomination met with disapproval from the Serbian government.
Ceku will keep almost all ministers who were in the government of his predecessor Bajram Kosumi.
Only former Deputy PM Adem Salihaj will no longer fill this post.
Opposition parties did not vote for Qeku's election, explaining that he would only make cosmetic changes to the government.
Qeku's successor at the post of Kosovo Protection Corps commander will be deputy commander Sulejman Selimi. The decision on Selimi's appointment was made by the UN Administrator in Kosovo, Soren Jessen Petersen, who also promoted him to the rank of Lieutenant General.