Schwarzenbauer led Audi's global expansion by increasing the brand's presence in the United States, boosting sales volumes in China and gaining market share across Europe while maintaining profitability.
He left Audi last August as part of a broader reshuffling of management by parent Volkswagen Group. Luca De Meo, a former chief marketing officer with Fiat, succeeded Schwarzenbauer at Audi.
Krueger, the BMW board's youngest member, was promoted from human resources boss to his current job last April. The automaker created the position by giving Krueger tasks previously overseen by BMW sales boss Ian Robertson.
Krueger is seen internally as a strong candidate to succeed BMW CEO Norbert Reithofer, who was head of the automaker's global production for six years before being named chief executive in September 2006.
Reithofer, who turns 57 in May, is under contract until 2016, at which time he'll be 60 years old, which is BMW's mandatory retirement age for its management board members.
Arndt began his career with BMW Group in March 1983. He ran the company's factory in Dingolfing, southern Germany, prior to being named to the management board in September 2006 as Reithofer's successor as BMW production boss.
Arndt said in a statement that he is leaving BMW "out of consideration for my health and my family, and out of responsibility towards the BMW Group."
BMW Supervisory Board Chairman Joachim Milberg in the same release credited Arndt with making "an enormous contribution" to the company. "We regret his decision, which he has made for personal reasons but, naturally, we respect it fully," he said.
At Audi, Schwarzenbauer helped the brand to expand sales. In his first year as sales chief in 2008, Audi crossed the threshold of 1 million in car sales. The brand's deliveries rose to a record 1.46 million cars in 2012.
Audi reported 2.77 billion euros (3.61 billion euros) in operating profit and a return on sales of 8.1 percent in the year he joined. Operating profit last year surged to 5.38 billion euros, with an 11 percent operating margin, making Audi one of the world's most profitable carmakers.
Schwarzenbauer left Audi, which is the largest earnings contributor at VW, in the wake of the management revamp. The reshuffle last year also triggered the departure of VW's former China chief Karl-Thomas Neumann, who became CEO at General Motors Co.'s Opel unit earlier this month, and Audi's former head of r&d Michael Dick.
Former Porsche U.S. boss
Schwarzenbauer was born in the Bavarian city of Weissenburg, Germany, and went to high school in Munich and Nova Friburgo, Brazil. After studying business administration at the Munich University of Applied Sciences, he joined BMW in 1984 and held several positions within the marketing and sales department.
He left BMW to join Porsche in 1994 and became CEO of the sports car maker's North American division in 2003. Five years later, he took over the management board position responsible for sales and marketing at Audi.
BMW and Audi are battling it out this year for the top sales position in premium autos, with the BMW brand securing a 407-car lead in the first two months of the year.
Bloomberg contributed to this report