Jan Ake Jonsson has worked for Saab for about 40 years.
As chief executive during the last six years, he was instrumental in saving Saab from closure.
"He's done an incredible job getting Saab back on track," Victor Muller, owner and chairman of Saab, told BBC World in an interview.
Mr Jonsson said: "The last three years have of course been very demanding and forced me to focus on one thing only - my work."Now it is time for me to also spend some time on other things that had to stand back for my duties to Saab."
The company is still struggling, however.
Spyker is selling its sportscar arm and will focus on expanding Saab Saab sold only about 30,000 cars last year, a slight improvement on 2009.
It hopes to sell about 80,000 this year, though the departure of Mr Jonsson will make this target harder to achieve, analysts said."This is certainly a negative," said Martin Crum at AEK."He is a very experienced manager and it will be very difficult to find a proper replacement. It will make it more difficult than before."
Mr Muller said the focus should be on profits rather than volume.
"We are constantly being confronted with sales targets, and this is logical because they're easy to measure," he said."But I'd rather sell 50,000 cars and make a profit."
Sportscar division sold
Spyker and its owner Mr Muller bought Saab last year from General Motors following major restructuring at the US car giant.Mr Muller insisted Saab is recovering and pointed to new models coming on stream soon."The launch of new products, the real pivot in this business plan is the launch of the new 9-3 in October 2012. That's the tipping point," he said."The company will have the widest and the newest product range the company has had in its entire 64 year history," said Mr Muller.Last month, Spyker announced plans to sell its sportscar arm and focus instead on expanding Saab.
It signed a provisional deal to sell the business to UK-based, Russian-owned, CPP Global Holdings for some 32m euros.