Michel Platini's announcement sparked jubilant scenes at Cardiff City Hall, after the bid won eight votes in the first round, compared with four for Italy and none for Croatia and Hungary.
World champions Italy were widely expected to win the right to host their first big tournament since World Cup 1990.
However, last summer's Calciopoli match-fixing scandal, along with repeated incidents of violence at Italian grounds, weakened their bid.
It is a risky choice, given the huge infrastructure and stadium improvements needed, along with the huge travelling distances across two large countries.
Additionally, it was believed that UEFA were not keen on having another joint host of the tournament following the Euro 2000 in Belgium and the Netherlands, and Euro 2008 in Austria and Switzerland.
However, it represents ambitious decision that reaches out to emerging areas of the continent and will provide a huge economic and social boost for both countries.
High-profile figures from both countries were deployed to promote the bid, including a Ukrainian contingent of Andriy Shevchenko, Sergei Bubka and Vitaly Klitschko.
Bubka said: "I'm very proud and happy and it will have a huge positive impact on the countries.
"There will not be a problem with the stadia, work on some new ones are already under way - one will be ready later this year and another next year.
"Everything will be done in time and the governments have promised the funding will be made available. This will accelerate the development of infrastructure in our countries."
Matches will be held in four cities from each country, with another four cities in reserve. Although significant improvements will take place at most grounds, only two stadiums - in Gdansk and Warsaw - will be built from scratch.
The Euro 2012 final is proposed for the Olympic Stadium in Kiev, which was built in 1923 but will be renovated and will hold 75,000 for the tournament.
Poland's Dutch head coach Leo Beenhakker said: "Eastern Europe has a great history in sport and in football and they still have great players but what they have been missing has been good infrastructure, stadiums and training facilities.
"Now the governments and the football federations are obliged to realise all their promises within the next five years and make these improvements.
"This is fundamental for football in Poland and Ukraine."
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