The Fed was among the first G7 countries to reduce borrowing costs by half a percentage point, shortly after the group said it was ready to take action, including fiscal measures where appropriate.
The pan-European STOXX 600 index closed up 1.4% after surging as high as 3.3% immediately after the rate cut.
Central banks in Britain, Japan and France have also signalled willingness to ease policy measures after a worldwide sell-off last week that erased more than $5 trillion from equity markets.
"The ECB is unlikely to follow through with a rate cut, but like the Fed, will start tweaking bank regulations to deal with what is a transient shock," said Sebastien Galy, senior macro strategist at Nordea Asset Management in Luxembourg.
"Central banks are by nature stabilizers in the system and the Fed is showing the way."
Growth-linked travel and leisure stocks ended 1.5% higher, after eight straight days of declines as widespread travel curbs to contain the outbreak crushed passenger numbers and dented demand at hotels.
Of the 21 European sub-sectors, only banks <.SX7P> closed out the session lower. Financial services companies tend to outperform in a higher interest rate environment.
The benchmark index is still about 12% shy of a February peak, reflecting the scale of the hit investors expect from the virus.
After a decade of cash injections from central banks, analysts also question if monetary stimulus will be enough this time round.
"The fear is that there is going to be a huge dip in consumer spending," said Jake Dollarhide, chief executive officer at Longbow Asset Management.
"This bull market is driven by the consumer so the coronavirus fear is that the consumer is going to be cut off from buying iPhones, steak dinners and Louis Vuitton."
Spanish banks powered a 0.8% rise for the Madrid bourse after the European Court of Justice ruled that it would be up to local judges to decide on a case-by-case basis if IRPH mortgage clauses were abusive.
Caixabank SA and Bankia rose 0.6% and 3.7%, respectively, on relief that the court did not decide on a blanket rejection of the clause.
Among individual movers, German wholesaler Metro soared 19.2% to the top of the STOXX 600 after U.S. food distributor Sysco contacted the company about a potential takeover, a person familiar with the matter told Reuters on Tuesday.
Qiagen NV jumped 17% after U.S. firm Thermo Fisher Scientific launched a 10.4 billion euro ($11.6 billion) bid for the German genetic testing company.
By Sruthi Shankar and Sagarika Jaisinghani
