"We feel that Ukraine is fully capable of doing the work (staging the finals)," UEFA president Michel Platini told a news conference on Monday.
"Therefore the executive committee has decided to split the finals equally between the cities in Poland and Ukraine (four and four). We are not going to change anything (from the original plan)."
Ukraine, in particular, has caused concern. It has been living under the threat of losing some of its venues as the building of stadium, roads, hotels and airports lagged behind schedule.
But European football's governing body ended those doubts on Monday when its executive committee approved the match schedule which included all eight cities - Warsaw, Wroclaw, Gdansk and Poznan in Poland and Kiev, Donetsk, Kharkiv and Lviv in Ukraine.
UEFA said that all eight cities would receive three group matches each while Gdansk, Warsaw, Donetsk and Kiev would also stage quarter-finals with Donetsk and Warsaw would stage semi-finals.
Kiev, as previously announced, will stage the final and Warsaw the opening match featuring Poland.
UEFA said that Poland would play their second group match in Warsaw and their third in Wroclaw while, Ukraine would play their first Group D match in Kiev and the other two group games in Donetsk.
UEFA had been frustrated by the slow progress of work in Ukraine, with Platini complaining of "huge infrastructure problems", and in May last year gave Donetsk, Lviv and Kharkiv six more months to show significant improvement.
In December, UEFA's executive committee said it was satisfied with the progress made and, to the huge relief of Ukrainian football officials and politicians, confirmed all four cities as hosts.
However, more doubts began to resurface earlier this year and Ukraine were given another warning by Platini in April over the slow pace of the work.
The following month UEFA's project director Martin Kallen said in a visit to Warsaw that Poland could host the tournament alone if Ukraine's stadiums were not ready in time but such drastic action has now been ruled out.
