Wheatcroft, who was formerly editor of the Sunday Telegraph, will be based in London, a press release said.
Before editing the Sunday title, she was business and City editor at The Times for almost a decade.
"The time has come for the Journal to take on the European market, in print and online. We have a world-class reporting presence in Europe and an unrivalled international business news franchise. The combination of these assets and Patience's extensive experience in media and business will make the Journal a formidable force in Europe," said Robert Thomson, managing editor of The Wall Street Journal and editor-in-chief of Dow Jones & Company.
Earlier this year WSJ Europe launched a new website under the editorship of former Guardian development editor, Neil McIntosh.
