London won 2.5 percent at the start and after closing up 7.5 percent on Tuesday.
At the open on Wednesday, Frankfurt jumped 3.7 percent, Paris won 3.1 percent, Milan gained 3.2 percent and Madrid advanced 4.0 percent.
"The stimulus is now by and large in place, the question is whether it's enough for the markets or whether the expected spike in cases and deaths in the US and Europe, combined with the emerging picture of the economic damage, means we need to take another leg lower before the bottom is found," Neil Wilson, chief market analyst at trading group Markets.com, said in a client note.
The latest major stimulus announcement came out of Washington, where US lawmakers agreed a package totalling around $2.0 trillion to support the world's biggest economy against the financial impact of the COVID-19 pandemic.