The 55-year-old Sejdiu is a senior official of the Democratic Alliance of Kosovo, the party which was led by Rugova until his death last month. He is a professor at the law school and the school of political science in Pristina and is fluent in French and English.
Of the 109 MPs taking part in the vote, 80 voted for Sejdiu in the third round.
Eight members of parliament representing Kosovo Serbs today continued to boycott the work of the assembly.
Addressing the parliament, the new Kosovo president said he would closely cooperate with other institutions and ruling and opposition parties in the UN-administered province.
He pledged to cooperate with all ethnic communities and residents of Kosovo so as to ensure the unity and democratic functioning of local institutions.
He said he was in favour of continuing cooperation with the United States, the European Union and the international Contact Group for Kosovo in a bid to make "Kosovo a state which has peaceful relations with its neighbours and which will guarantee all human and minority rights in line with the highest standards of the democratic world".
He called on local Serbs to join efforts to establish a democratic, prosperous and tolerant Kosovo.
Sejdiu announced that he would play a leading role in a team to negotiate with Serbia about the future of the province. The UN-sponsored negotiations should soon start in Vienna.
Serbian President Boris Tadic congratulated Kosovo Albanians on the election of Sejdiu as the new president.
"Mr. Sejdiu, my door is open to you so that we can launch direct talks. We must immediately start solving everyday problems of Kosovo citizens," Tadic said in his telegram.