"In the days ahead, the attention of the world will be focused on our country. I urge you to show full Ukrainian hospitality, sincerity and friendliness," Yanukovich said in an address to the nation.
Ukraine, which is co-hosting the tournament with Poland, has suffered a deluge of bad publicity before the kick-off on Friday. Yanukovich made no reference to criticism from Western governments and media over the government's treatment of opposition leader Yulia Tymoshenko.
Many European Union politicians are threatening to boycott matches because of the jailing of Tymoshenko on a charge of abuse of office. Western governments say she is the victim of "selective justice".
In London, the British government said its ministers would boycott the group stage of the tournament because of human rights concerns. England play their three Group D games in Ukraine.
"No ministers will be attending group games at Euro 2012," a foreign ministry spokesman said.
"We are keeping attendance at later stages of the tournament under review in the light of ministers' busy schedules ahead of the Olympics and widespread concerns about selective justice and the rule of law in Ukraine."
Reports in the British press of racist attacks at Ukrainian football club matches have added to bad publicity over high-level corruption and excessive hotel prices.
Yanukovich congratulated Ukrainians on building modern stadiums, laying thousands of kilometres of new roads and upgrading rail and airport facilities.
"Five years ago... no one believed that our country would have managed to prepare for the hosting of such a large-scale event," he said.
"We should correctly welcome guests and participants of the championship. The tourist future of our country will depend on how they remember Ukraine and Ukrainians," Yanukovich said.
Apart from Kiev, Euro 2012 matches will be played in the Ukrainian cities of Lviv, Kharkiv and Donetsk.
