EU citizens are not required to register with the Ukrainian authorities upon arrival. However, they are required to declare any cash or other valuables they bring into the country in excess of a certain amount.
For stays longer than 90 days, EU citizens must apply for a temporary residence permit from the State Migration Service of Ukraine. The application must be submitted within 90 days of arrival in Ukraine. The temporary residence permit fee is 125 USD.
For more information about visa requirements for Ukraine, please visit the website of the Ukrainian Ministry of Foreign Affairs.