"The supporters from Ireland and Northern Ireland have distinguished themselves by their exemplary attitude, fair play and good mood," the statement read.
Both governments have been informed and an official ceremony featuring fan groups from both teams will take place in the next few days, the statement added.
Ireland and Northern Ireland lost to France and Wales respectively in the round of 16. The fans from both teams have won praise from all sides for their joyful and friendly behaviour during the tournament.
UEFA's interim General Secretary, Theodore Theodoridis, said on Tuesday that the passion of some of the fans and their supporters would be rewarded in some way.
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"We have seen some amazing scenes and we really want to show and emphasise the positive side of football", he said.
Euro 2016 has been largely incident-free since violent clashes marred a group game between England and Russia in Marseille early in the tournament.
(Reporting by Patrick Vignal and John Irish. Editing by Adrian Warner.)
