Ukraine will co-host the tournament with neighbouring Poland but doubts were raised by Uefa president Michel Platini when he visited the host cities early last year.
Platini questioned their preparation and announced they may be stripped of the position if they could not start hitting targets.
Kiev's Olimpiyskiy stadium, which is being renovated and updated, and Lviv emerged as the main talking points after Platini's visit last April.
But at a press conference marking one year to go until the opening game of the tournament, Infantino said: "It is impressive what is going on in Ukraine.
"There are many milestones but we are now on the final straight and have achieved much in Poland and Ukraine.
