U.S. President Donald Trump said he had replaced Tillerson with Central Intelligence Agency Director Mike Pompeo, and had tapped Gina Haspel to lead the CIA.
Europe's STOXX 600 <.STOXX> fell to a session low, down 0.3 percent on the news. The pan-European banks index <.SX7P> also tumbled to the day's low, down 0.2 percent.
Yields on safe-haven bonds in the euro zone also fell, with Germany's 10-year bond yield touching a fresh 1-week low at 0.608 percent <DE10YT=RR>.
The dollar, meanwhile, extended its fall. It had already been weak across other G10 currencies after U.S. inflation data came in as per forecasts but it skidded further as the sell-off accelerated.
Against a basket of currencies, the dollar fell 0.2 percent <.DXY>, while the euro gained 0.3 percent to $1.2369 <EUR=>. The greenback gave up half of its gains versus the Japanese yen <JPY=>, with the pair last trading at 106.83, the yen down 0.4 percent on the day.
(Reporting by the London Markets Team; Editing by Sujata Rao)