The pan-European Stoxx 600 index climbed to close over 1.3 percent higher, with all major bourses rallying more than 1 percent on the news that international officials have started to work on a "staff level agreement" with Greece.
Traders cheered the hints of a tentative deal, after months of drawn out bailout talks between Greece and its international bailout supervisors, propelling the French CAC index to close around 2 percent higher and Greek stocks to end around 3.5 percent higher.
Greek Prime Minister Alexis Tspiras said he was "close to an agreement" in a statement and that the deal would be positive for the Greek economy, adding there was "absolutely no danger" to pensions, salaries, banks or deposits in the potential deal.
On Tuesday, Greece and its Europeans creditors sought to play down fears that Athens would default on a June 5 debt payment to the International Monetary Fund.
Aer Lingus shares closed around 2.6 percent higher after the Irish government agreed to sell its 25 percent stake in the airline to , the owner of British Airways.
Shares in IAG finished up over 3 percent on the FTSE on Wednesday, making it one of the best performers on the index. The other best performers were Imperial Tobacco and Shire, whose share prices target was raised by Deutsche Bank.
Shares of luxury goods maker LVMH ended around 1.2 percent higher after a report that the group was in talks to buy the French newspaper Le Parisien from media group Amaury, as it looks to strengthen its media business.
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