The Arlington-based U.S. business of BAE Systems said Tuesday that Linda P. Hudson, its president and chief executive, will step down early next year.

Hudson, who has led BAE since 2009, will remain on the board of the U.S. unit through April 2015, according to the announcement. The company said its board will conduct a search for a successor.

Hudson was the first woman to lead a major U.S. defense contractor. She joined BAE in 2007, taking over its land and armaments business as the market for armored vehicles surged.

But she has spent much of her time at the helm of BAE repositioning the company for shrinking government budgets. Hudson has divested some lines of business, reorganized the company’s structure and opened a shared services center in North Carolina.