The measures could come into effect within days.
French Foreign Minister Jean-Yves Le Drian confirmed on Tuesday that EU sanctions against Russia had been "unanimously agreed to" by the bloc's top diplomats.
EU foreign affairs chief Josep Borrell said the raft of penalties "will hurt Russia, and it will hurt a lot.''
The measures will target the 351 lawmakers who voted in favor of the recognition, along with 27 individuals and entities who threaten Ukrainian territory and sovereignty, Borrell said.
These include figures from Russian business, media and politics, what Borrell referred to as "oligarchs."
A draft proposal of the sanctions said all those who were involved in the "illegal decision" in Ukraine would be personally targeted by sanctions.
Banks financing the Russian military and other operations in those territories are also included.
The measures will now be formally approved by Brussels as part of the EU's response to Russian President Vladimir Putin's recognition of two breakaway regions in eastern Ukraine. Putin himself was not on the sanctions list.
"Our action today is a response to Russia's aggressive behavior," European Commission President Ursula von der Leyen said of the sanctions.
"If Russia continues to escalate this crisis that it has created, we are ready to take further action in response", she added, also stressing the need for the EU to be less dependent on Russia for gas.