Now comes the hard part.
Tadic's February 3 second-round triumph will almost certainly earn him the distinction of being the Serbian president who ended up losing Kosovo.
During his campaign, Tadic -- like Nikolic -- repeatedly said he would never recognize statehood for the breakaway ethnic-Albanian province.
But if the newly reelected president wants to fulfill his long-standing dream of steering Serbia into the European Union, he also understands that an independent Kosovo is part of the package.
Speaking in Brussels the day after the vote, EU foreign-policy and security chief Javier Solana said he is ready to continue working with Tadic toward that end.
"We will continue working with Serbia," Solana said, "and we would like Serbia to get as close as possible, as rapidly as possible, toward the European road, which is to my mind what the majority of people want."
Polls in fact show a large majority of Serbs want to join the European Union -- but an equally large majority also wants to avoid giving up Kosovo.
For this reason, the coming weeks will see Tadic navigating perilous political waters. The Kosovar leadership is impatient to receive what they see as their right to statehood. Much of the international community -- at least the United States and Europe -- views independence for Kosovo as a foregone conclusion.
Inside Serbia, however, most members of Tadic's fragile coalition government -- particularly Prime Minister Vojislav Kostunica -- are staunchly opposed to the notion.
Analysts say that Tadic's most immediate task will be holding his governing coalition together, and ensuring that Kostunica -- who as prime minister wields greater power than the president -- does not run EU integration off the rails.
In December, Serbia's parliament passed a resolution calling for Belgrade to cut off diplomatic relations with any state -- including the European Union -- that recognizes Kosovo's independence.
Although some member states have expressed reservations, the EU -- like the United States -- has expressed general support for Pristina's independence bid. If Serbia honors its December resolution, it will find itself isolated from two major partners.
Kostunica is due to meet EU officials on February 7 to sign a series of preliminary agreements aimed at securing a key Stabilization and Association Agreement with Brussels that is seen as a key step toward eventual membership.
Speaking to RFE/RL's South Slavic and Albanian Languages Service, Cedomir Cupic, a political science professor at Belgrade University, says this week's talks may prove so divisive that it could force the dissolution of the Serbian government and a call for early parliament elections.
"I assume it will be resolved soon," Cupic says. "We already have a meeting scheduled for February 7 to sign part of the agreement with the EU. This will show us how the prime minister is going to handle this. If some divisions become apparent, then we may have parliamentary elections in the spring."
Analysts say that Kostunica has in the past skillfully played on Western fears of a Nikolic victory to argue against Kosovo's independence.
"This is a strategy that has been used especially by Prime Minister Kostunica, who has for several years used this strategy of trying to somehow threaten the international community that if concessions are not made to Serbia, then [Nikolic's] Radicals will come to power," says Sabine Freizer, director of Europe Programs for the Brussels-based International Crisis Group. "But I think now this strategy has somehow come to an end. The European Union -- and the rest of the international community -- will most probably move forward on the Kosovo question."
The Pristina Effect
Should Serbia's government fall and new parliamentary elections be called, Nikolic's Radical Party would again be poised to win a large share of the vote -- and the fears Kostunica has so deftly exploited would be right back on the table.
Such an outcome could further muddle both Kosovo's independence bid and Serbia's drive to join the EU.
Meanwhile, Kosovar leaders say they are pressing ahead with plans for independence. In Pristina, Prime Minister Hashim Thaci said he expects Serbia and Kosovo to cooperate "as two independent states in regard to our Euro-Atlantic integration priorities."
Thaci added that the only question remaining is the formal date for an independence declaration, which is currently being negotiated with the EU.
Parliament speaker Jakup Krasniqi said he expects the declaration to come this month. He also said the outcome of Serbia's presidential vote should have no bearing on Kosovo's move toward independence.
"I can say that these elections have no effect on Kosovo," Krasniqi said. "The only influence it could have is the fact that the winner is the pro-European candidate, he is the most democratic candidate -- if we can call it that -- in Serbia. This candidate wants to integrate Serbia into the European Union, and from this perspective this also interests us."
The timing of Kosovo's declaration is a critical issue for Brussels. Freizer explains that the EU is trying to ensure that the process is carefully managed to prevent instability.
"What I think is most important is for the declaration of independence is that it be a managed process," Freizer says. "So here, what is important is that Pristina really declares independence at a time when the European Union, and the United States, are ready for that."
Freizer warns that "there are a few things that need to be done before Pristina could declare independence in this kind of managed transition." He says first among those measures is that the European Union must "adopt joint actions, to assure the deployment of a mission to Kosovo."
But against this backdrop, Kosovar Albanians -- as well as their leaders -- are growing increasingly restless and impatient with what they see as many false starts on the road to statehood.
"There is fatigue in the sense that people are a little tired of setting dates," according to RFE/RL's Pristina bureau chief, Arbana Vidishiqi. "Certainly they know that this is a process that cannot be turned back anymore. But people are tired of these dates, they just want to get on with it."
Ironically, the pro-Western Tadic's victory appears to have actually slowed down the time frame for a formal independence declaration.
"The small impact that it can have has to do with setting the date for a declaration of independence," says Ilir Dugolli, a Pristina-based political analyst with the Kosovar Institute for Policy Research and Development. "Nikolic's victory would have speeded up this process by weeks, maybe, while Tadic's victory brings back the scenario of waiting for a joint decision of the EU bloc for assigning a new mission in Kosovo and for recognizing the independence declaration."
KFOR, the NATO-led peacekeeping mission in Kosovo, has reinforced its troops and is on alert in case of any possible violence in the province.
(RFE/RL's South Slavic and Albanian Languages Service contributed to this report.)