In initial deals, London's benchmark FTSE 100 index of major blue-chip companies won 2.5 percent to 5,552.32 points compared with Friday's closing level.
In the eurozone, Frankfurt's DAX jumped 3.9 percent to 9,896.66 points and the Paris CAC 40 leapt 3.4 percent to 4,295.46.
Milan's FTSE Mib added 3.3 percent to 16,925.05 and Madrid's IBEX 3 rallied 3.0 percent to 6,777.50 points.
"European markets are trading higher because investors are shrugging off the pessimism," said AvaTrade analyst Naeem Aslam.
"They are focused on more optimistic things: the slowing death rate caused by coronavirus.
"Italy, Spain, France, and Germany have all seen declining numbers.
"Some optimism does exist in New York's death numbers too, but it may be premature to comment on anything further because the infection rate is still on the rise in New York."