Frankfurt jumped 2.4 percent, Paris gained 1.9 percent, Milan won 2.0 percent and Madrid climbed 1.7 percent.
Outside the eurozone, London advanced 2.2 percent, with all eyes also on whether OPEC and its partners will announce a cut in oil output after a meeting Thursday.
"Despite some pretty awful coronavirus statistics traders are optimistic that the outbreak is nearing its peak and that governments would roll out more stimulus," said City Index analyst Fiona Cincotta ahead of a long Easter weekend.
"A jump in oil prices amid expectations of an output cut at today's OPEC meeting is also playing its part" in lifting stock markets, she said.
Top crude producing nations will hold a crucial teleconference after a collapse in oil demand caused by the coronavirus and a damaging Saudi-Russia price war sparked a crash in the market.
The talks between OPEC and its non-member allies, notably Russia, is seen as the best chance to provide some much-needed support to crude prices wallowing around two-decade lows.