The legislation, which also targets Nazi propaganda was adopted by 254 votes in favour in the 450-member parliament, or Rada.
It bans all symbols and propaganda representing "the totalitarian Communist and Nazi regimes" -- from street names and flags, to monuments and plaques.
For the former Soviet republic it could mean a major overhaul of public buildings and town squares across the country, with Lenin Streets to be renamed and any remaining statue of the Soviet leader removed.
The fate of the Communist leader Lenin's many statues became the focus of debate during the late 2013 Maidan protests that led to the ouster of then pro-Russian president Viktor Yanukovych and sparked events that led to the war in the east.
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As pro-Western protesters toppled Lenin effigies in rage, pro-Russian separatists in the east gathered at their feet.
"The USSR was a great country," separatist leader Alexander Zakharchenko told AFP in the rebel bastion Donetsk, echoing President Vladimir Putin who has dubbed the collapse of the Soviet Union "the major geopolitical disaster of the century."
Putin is accused by the West of arming the east Ukraine rebels to stop Ukraine looking to the EU and NATO for partnership, an allegation denied by Moscow.
A list of banned items includes the Soviet flag and anthem as well as monuments and historical plaques commemorating Communist leaders. Penalties for violating the law range from five to 10 years.