Grocery giant Aldi plans to add 800 new stores in the U.S. over the next five years.

The German-owned, Illinois-based chain said in a release Thursday it plans to build or expand hundreds of Aldi locations in the company's existing Northeast and Midwest strongholds, as well as in the western U.S. and Southern California. A first Las Vegas location is planned, too.

Meanwhile, in the Southeast, the company will convert many Winn-Dixies and Harveys locations into Aldis, though "a meaningful" number of them will remain under their current brands. Aldi said Thursday its acquisition of Southeastern Grocers, the parent company of Winn-Dixie and Harveys, had been completed.