The activists hope to draw attention to EU's "murderous exterior walls" that have over the years claimed several thousand lives.
The white cross-shaped signs carry the names of several people who lost their lives while fleeing from East Germany before the fall of the Berlin Wall.
The signs were pulled out from their frames on the south bank of Berlin's Spree River and have been scattered across several EU borders, including Bulgaria.
"We have moved the crosses to safety," said spokesman Philipp Ruch of the German artistic group 'Center for Political Beauty'.
The activists are also planning to travel to a secret place along the EU frontier, "to dismantle the borders with bolt cutters," to coincide with the weekend-long celebrations marking 25 years since the fall of the Berlin Wall.
In an online statement, the group posted: "While in Berlin balloons will rise into the air and nostalgic, sedative speeches will be held, German civil society will in an act of political beauty bring down the European external walls ... the European Curtain must fall."
Berlin police are investigating the move as a "severe case of theft" with "a political motivation."
Meanwhile, over 21 people drowned on Monday after an overloaded boat carrying migrants towards EU waters sank just off Istanbul, near the Black Sea end of the Bosphorus strait, Turkish officials reported.