The decision followed a pronouncement last week by French Foreign Minister Laurent Fabius urging the EU to take "ultra-rapid" action in Mali because all of Europe was threatened by terrorism, The Wall Street Journal reported.
The mission, which is expected to include a protection force of several hundred other troops, should be ready in February, said Luxembourg Foreign Minister Jean Asselborn.
The mission aims to train four combat units of Malian troops.
Nearly 1,000 French troops have been dispatched to Mali, and French warplanes have struck a rebel-held town in central Mali.
German Foreign Minister Guido Westerwelle said his country would provide logistical help. Germany will send two aircraft but no troops, he said.
Westerwelle said African troops have principal responsibility for the situation in Mali.
The foreign ministers also are expected to consider other financial support for Mali, such as restarting development aid that was suspended after last year's coup.