But it threatens to worsen ethnic tensions between Kosovo's Albanians and Serbs. Security in the divided northern town of Mitrovica was high a day after a gunman attacked a police station, wounding one officer.
Kosovo's ethnic Albanian leaders are to mark the constitution in a low-key ceremony in Pristina later Sunday that will open with Kosovo's newly approved, instrumental anthem.
President Fatmir Sejdiu called it the most important act since Kosovo's declaration of independence in February.
"This is a historic moment for Kosovo," Sejdiu told reporters after being handed the charter by assembly leader Jakup Krasniqi. "This marks the closing of Kosovo's cycle of statehood."
However, Serbs - who make up less than 5 percent of Kosovo's population of 2 million - strongly oppose the ethnic Albanian leadership's decision to declare independence from Serbia after U.N.-mediated talks fell through last year.
The U.S., Japan, Britain and some 40 other nations have recognized Kosovo's move but Serbia, its ally Russia and others have called the declaration illegal under international law. Serbia - which considers Kosovo its historic and religious heartland - insists it still belongs to Belgrade.
"Serbia views Kosovo as its southern province," Serbian President Boris Tadic said Sunday. "It will defend its integrity by peaceful means, using diplomacy, without resorting to force."
Tadic said his government will insist on a new round of internationally mediated talks on Kosovo.
"This will be our strategy and our response to the proclamation of an illegal state in Kosovo," he told reporters Sunday in Belgrade.
In an attempt to undermine Kosovo's independence and the ceremony in Pristina, Serbia's top official for Kosovo, Slobodan Samardzic, shunned the ceremony in Pristina, instead visiting the ethnically divided town of Mitrovica.
Samardzic is expected to promise an assembly for the Serb-dominated north, the region of Kosovo bordering Serbia - a move that would bring Kosovo closer to a partition along ethnic lines.
Sejdiu said the constitution assures Kosovo's minorities broad rights. He called it "an important message for the international community and the European Union that Kosovo is a democratic country."
Britain's Foreign Secretary David Miliband called Kosovo's new charter "an important further step along its path away from conflict and towards achieving a democratic, multi-ethnic and European future."
The plan to shift Kosovo to government control envisaged a European Union team acting as overseers and taking over from the U.N. administration, which stepped in following a 78-day, NATO-led air war in 1999 to stop former Yugoslav leader Slobodan Milosevic's crackdown on ethnic Albanian separatists.
An estimated 10,000 people, mostly ethnic Albanians, died in the Serb crackdown.
However, Russia blocked the EU from taking on the role, prompting the U.N. to stay in charge of Serb areas while gradually handing areas over to the EU's police officers, judges and advisers. Russia said it considers the 2,200-strong EU mission illegal because it has not been approved by the U.N. Security Council.
Since 1999, Kosovo's majority ethnic Albanians and minority Serbs have struggled to bridge their differences. Most of Kosovo's 100,000 remaining Serbs live in the north in a region separated from ethnic Albanians by a river.
Having two international missions on the ground - the U.N. dealing with Serbs and the EU with ethnic Albanians - will only widen the ethnic divide, said Agron Bajrami, editor-in-chief of the ethnic Albanian daily newspaper Koha Ditore.
"We are entering a process that is a very risky one in terms of having two international missions, with two different realities ... one as perceived by the Albanian community and one as perceived by the Serbian community," Bajrami said. "That could lead to the division of Kosovo."
Amid fears that tensions could spill over into the rest of the Balkans, NATO deployed 600 more British troops to the north to join some 16,000 peacekeepers.