Thaci, 39, who was elected by a vote of 85-22, said: "Our aim is to make Kosovo independent in the first part of this year. We will make our dream and our right come true soon ... Kosovo will be independent."
Sejdiu, who took over the presidency after the death of Ibrahim Rugova in January 2006, was re-elected under a power-sharing deal between his Democratic League of Kosovo (LDK) and its main rival, Thaci's Democratic Party of Kosovo (PDK).
Any unilateral proclamation of independence is likely to be approved by the US and a number of European countries, but Serbia and its ally Russia say they will would oppose any such move.
After his election, Sejdiu said: "Independent Kosovo, which will soon get international blessing, will be fully devoted to development and cooperation with all countries in the region."
He said that "special attention" will be paid to the province's Serb minority and its full integration in Kosovo and its institutions.
The cabinet presented by Thaci late on Tuesday gives seven posts to his PDK, and five to Sejdiu's LDK.
One vice-premier's position goes to each party, with three additional posts for representatives of minorities, including two for the 100,000-strong Serb community, which overwhelmingly boycotted the November polls.
The parliament earlier elected Jakup Krasniqi of the PDK as its chairman.
Kosovo has been run by the UN since 1999 when a Nato bombing campaign drove out Belgrade's forces which had been waging a crackdown on independence-seeking ethnic Albanians who make up 90 per cent of the population.