The EU's diplomatic chief, Javier Solana, described Sedjiu's election by the Kosovo parliament as a sign of maturity and unity.
European Enlargement Commissioner Olli Rehn also congratulated Sedjiu.
Sejdiu, the candidate of the Alliance for a Democratic Kosovo (LDK), was elected on the third round of balloting, with an 80-vote majority.
He was a close associate of the late President Ibrahim Rugova, who died last month of lung cancer.
In his acceptance speech today, Sejdiu vowed to pursue Rugova's goal of independence for the province.
He urged all of Kosovo's citizens to work together to make the province a place where human rights and the highest democracy standards are respected.
UN-mediated talks on Kosovo's final status are due to begin in Vienna on 20 February.
THE WORLD'S NEWEST NATION? The region of Kosovo has a population of more than 2 million, some 90 percent of whom are ethnic Albanians. It was one of the poorest regions in the former Yugoslavia, but has considerable mineral wealth and an enterprising population, many of whom work abroad but keep close contact with Kosovo. All ethnic Albanian political parties seek independence on the principles of self-determination and majority rule. They feel that Serbia lost its historically based claim to what was its autonomous province under the 1974 constitution by revoking that autonomy in the late 1980s and then conducting a crackdown in 1999 that forced some 850,000 people to flee their homes.
Since NATO's intervention that year to stop the expulsions, Kosovo has been under a UN administration (UNMIK). The UN has begun to gradually transfer functions to elected Kosovar institutions. The primary Serbian concerns are physical safety for the local Serbian minority, a secure return for the tens of thousands of Serbian displaced persons, and protection for historic Serbian religious buildings. The main problems affecting all Kosovars, however, are economic. Until Kosovo's final status is clarified and new legislation passed and enforced, it will not be able to attract the investment it needs to provide jobs for its population, which is one of the youngest and fastest growing in Europe. Prosperity is widely seen as the key to political stability and interethnic coexistence in Kosovo, as is the case in much of Southeastern Europe.
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