At a ceremony in Warsaw the president of European football's governing body, Michel Platini, presented Pawel Michalczak, a 34-year-old forester who lives near the Polish capital, with his prize of a ticket for Poland's three first-round matches.
"Of course I can't guarantee you'll get to see them in the second round too," Frenchman Platini joked, speaking in Italian as his former Juventus team-mate and ex-Poland icon Zbigniew Boniek translated.
Michalczak won a competition organised by UEFA for Polish fans.
"I couldn't believe it when I got the call. I thought someone was trying to sell me something," Michalczak said.
"Then I thought it was my friends playing a bad joke. Now I'm just really happy," he added, revealing that he failed to get tickets for the 2006 World Cup in Germany and Euro 2008 in Switzerland and Austria.
Platini drew the name of a second Poland fan, Ewa Lewczuk, at the ceremony and telephoned her live from the stage.
"This is fantastic. It's not a joke?" said Lewczuk as she learned she would get four tickets for Poland's June 8, 2012 game in Warsaw, which kicks off the entire tournament.
"My husband and son are massive fans. And I'm overwhelmed," she added.
In a ceremony in Kiev, capital of Poland's fellow host nation, Ukraine, UEFA executive member Frantisek Laurinec handed over four tickets for the country's June 11 opener to primary school teacher Vita Lavrenko, who was accompanied by her young son.
Other fans hoping to see the 16-nation championships will also need luck.
More than 550,000 tickets are available for the general public but demand traditionally far outstrips supply -- 10.4 million people applied for 300,000 tickets at Euro 2008.
From Tuesday until the end of this month, would-be buyers must sign up at a ticket portal on UEFA's website, uefa.com.
UEFA underlines that the site is the only authorised channel, and warns that other purported sources could be fronts for rip-off merchants.
"We will be vigilant and will take all necessary measures against fraud," Pedro Correia, head of UEFA's ticket operations, said in Kiev.
In April, UEFA will decide by lottery who gets to purchase a ticket.
On Tuesday, 591,000 people had already applied, 70 percent from Poland and Ukraine, and the rest from 159 other countries, UEFA said.
The portal was swamped, the screen displaying a message that tickets will not be sold on a first come, first served basis.
UEFA's ticket sales manager, Rainer Berak, hammered home that point in Warsaw.
"There's no danger of missing out if you don't rush to the portal today. You can apply in the next few days or weeks and you'll have the same chance. You've got the whole of March," he said.
Tickets are a money-spinner for UEFA, and Correia said they were set to generate 100 million euros.
UEFA says it has taken Poles' and Ukrainians' lower spending power into account.
The average monthly gross salary in Poland is around 800 euros, and in Ukraine, just over 200 euros. That compares with the equivalent of 4,000 euros in Switzerland and 2,000 euros in Austria.
The cheapest 2008 ticket was 45 euros. The bottom rung in 2012 is 30 euros.
At 600 euros, the cost of high-end tickets is unchanged.