England, which has never won the tournament, was drawn Friday into Group D and will play France, Sweden and co-host Ukraine.
The Netherlands, also based in Ukraine, opens what appears to be a difficult Group B against Denmark, then meets Germany and Portugal.
Poland hosts Greece in the tournament opener on June 8, then plays Russia and the Czech Republic in Group A. which many see as the weakest group.
The final of the 16-national tournament is July 1 in Kiev.
Expected large traveling fan groups from Germany and the Netherlands could have logistical challenges with their teams playing in Ukraine.
Even before the draw, England committed to a base hotel in Krakow, Poland.
Spain, which also won in 1964, is seeking to become the first repeat champion. The Furia Roja also are the defending World Cup champions.