The special tribunal will be created through an agreement between Ukraine and the Council of Europe, the continent's top human rights body.
Zelenskiy visited the Strasbourg-based organisation for the first time as part of the announcement.
The special tribunal aims to target senior Russian leaders for the "crime of aggression", which underpins the countless war crimes Ukraine accuses Russian forces of committing since the start of the war on February 24, 2022.
Existing international courts, including the International Criminal Court in The Hague lack jurisdiction to prosecute Russian nationals for that specific offence.
Since early in the conflict, Kyiv has been pushing for the creation of a special tribunal that goes beyond prosecuting war crimes that Ukraine alleged Russian forces committed, including bombing civilian infrastructure, killing civilians, rape, taking hostages and torture. Russia denies those accusations.
There are logistical details still to be resolved, including where the court will be based. The Hague has been suggested because of its existing legal infrastructure, but no final decision has been made.
Russia does not extradite its own citizens, and whether or not Russian President Vladimir Putin will ever end up in the dock remains to be seen.
Under international law, sitting heads of state and certain other top officials - often referred to as the "troika", including a country's head of state, head of government and foreign minister - enjoy immunity from prosecution.
That means any potential indictment of Putin could only move forward if he leaves office.
There is no statute of limitation on the crime of aggression.
The institution will be funded by supporting countries known as the Core Group, including the Netherlands, Japan and Canada.
The United States backed the project under former president Joe Biden, but President Donald Trump's administration did not support the initiative.
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