According to a source quoted by Reuters, Wheatcroft will take over from Daniel Hertzberg, who is retiring after more than three decades at the paper.
Wheatcroft, who is a non-executive director of Barclays and central London property developer Shaftesbury, has worked for a News Corporation-owned title previously -- as business and city editor of The Times from 1997 to 2006.
During her stint at The Times, she worked with its former editor Robert Thomson, who is now editor of the Journal.
The appointment is seen as an attempt by News Corp to raise the profile of the Journal's European edition.
Wheatcroft worked at the Sunday Telegraph in 2006 and 2007 before joining Barclays. She was replaced at the Telegraph by its deputy editor Ian MacGregor.