The 55-million-euro (USD 60 million) museum features badges from the successful "Leave" and doomed "Remain" campaigns along with a ballot from last June's Brexit referendum.
But they form only a tiny part of a collection that stretches back through the turbulent history of the continent, focusing mainly on the 20th century.
Exhibits cover the two world wars and the Holocaust through the Cold War and the formation of the European Union, to the present day.
"Here we do not have a line to take. There are many different messages, our history and our heritage is here, our problems and disasters too," he told a news conference.
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"But by studying the past we can have a better future."
Museum board of trustees chief Hans-Gert Pottering, himself a former EU parliament head, said the exhibition celebrated European "values" at a time when growing populism and instability calls them into question.
Pottering said the decision to include exhibits from Britain's June 2016 vote to become the first country to leave the EU had been taken by museum staff without any outside influence.
"This shows to you that the team was totally independent," Pottering said.
He added however that former British premier David Cameron, who called the referendum, was a "very tragic person, what he has done to Europe and especially to his own country."
It also includes a bright red t-shirt of the Leave campaign.
The museum, which will be free to the public, however contains almost no labels explaining the exhibits as visitors instead get a tablet computer which can locate their position in the galleries - available in 24 languages.
It is located in the Eastman building - originally a dental clinic set up by Kodak founder George Eastman in 1935 in the scenic Parc Leopold in the European quarter of Brussels.
The collection contains 1,500 objects from 300 museums across Europe and beyond.
Taja Vovk van Gaal, academic project leader of the museum, admitted that it had been challenging to settle on a format for a collection that covers so many countries.
"It has been rather hard to tackle the question of what European history is and how it can be presented now in the museum," she said.
"The collection policy was trying to get different perspectives on the same event. The same happened for the referendum on Brexit," she added.