In a letter accompanying the formal acceptance, Ukraine's Parliament accused "senior officials of the Russian Federation" and rebel leaders with atrocities during the annexation of Crimea and fighting in eastern Ukraine.
The letter alleged that "thousands of Ukrainian nationals, including children, were killed," thousands more injured and hundreds of thousands forced to flee their homes.
While Ukraine is not a member of the court, it can voluntarily accept its jurisdiction.
Russia also is not a member, but any of its nationals suspected of committing a crime in Ukraine could now face prosecution.
Last year, Kiev filed a similar declaration accepting the Hague-based court's jurisdiction for possible crimes committed from November 2013 until February 2014, opening the way for a preliminary probe into the violent crackdown by former President Viktor Yanukovych's regime on demonstrators.
Prosecutor Fatou Bensouda will likely now expand that probe to cover possible crimes committed in Crimea and the country's conflict-hit east.
Government forces have been battling Russia-backed separatist rebels for months in eastern Ukraine.
Roman Romanov, director the Ukrainian non-government group International Renaissance Foundation, welcomed the move.
"Ukraine has taken a crucial step towards ending violence and armed conflict in the east of the country," he said in a written reaction.
"The next step is for national investigations to be stepped up and for Ukraine's full cooperation with the ICC. Peace comes not when the guns are silent, but when justice is done."