He has been replaced by chief executive of Aldi Austria, Armin Burger.
The company says the departure has been made “by mutual consent”, with Foley moving on to “pursue new business interests”.
It comes at a time when sales growth for the discount chain and competitors such as Lidl have seen a dramatic slowdown.
According to TNS Worldpanel, in the three months to 12 July Aldi’s sales grew 8.3%. This was compared to growth of 17% a year earlier.
Last year, Aldi reported a strong 25% increase in second quarter sales, attributing it to the continued pressure on consumer spending.
It also saw sales surge by 44% in July 2008 compared to the same month the previous year.
The retailer said at the time the figures showed that consumers were switching from their traditional supermarkets to lower-cost alternatives, as they faced rising household bills.