All 27 EU leaders have agreed a €50bn aid package for Ukraine after Hungary had previously blocked the deal.
Ukrainian President Volodymyr Zelensky welcomed the new funding, saying it would strengthen the country's economic and financial stability.
Ukraine's economic ministry said it expects the first tranche of funds in March.
There had been fears Hungary's PM would again block the package as he did at a European summit last December.
Viktor Orban, Russian president Vladimir Putin's closest ally in the EU, had said he wanted to force a rethink of the bloc's policy towards Ukraine and questioned the idea of committing to fund Kyiv for the next four years.
The package will help to pay pensions and salaries and other costs over the next four years. It comes as US military aid for Ukraine is being held up by Congress.
News of the agreement was announced less than two hours after the summit started, surprising many observers who had expected talks to go on much longer due to the depth of disagreement between Mr Orban and the other EU leaders.
Diplomatic sources told Reuters that the new deal includes a yearly discussion of the package and the option to review it in two years, "if needed".
Mr Orban had been pushing for a yearly vote on the package, but this could have left the deal exposed to an annual veto threat from Hungary.
"A good day for Europe," Ursula von der Leyen, the president of the European Commission, said on X.
Ukrainian President Volodymyr Zelensky said he was "grateful" to EU leaders, highlighting that the decision was taken by all 27 heads of state. He also said that the package would "strengthen the long-term economic and financial stability" of Ukraine.
The funding was important for Ukraine financially - and because it needs Europe to stay united in its support.
Ukraine's Foreign Minister Dmytro Kuleba had underlined that it was about Europe investing in its own security. He stressed that Ukraine was resisting Russia for everyone - blocking Vladimir Putin's attempt to challenge the world order by force.
Polish Prime Minister Donald Tusk, who had been highly critical of what he called Mr Orban's "strange and egotistic game," posted on X: "Viktor Orban could be 'persuaded'... Let's move on."