Mr Kerr, widely credited with having turned Edexcel around after taking over when the board faced a crisis in 2001, took an undisclosed redundancy payment last month. As he took over, the board had been criticised for a string of exam mistakes. It also faces a large deficit.
Stephen Mullarkey, previously finance director at Edexcel, has also left.
Edexcel said Mr Kerr was leaving to pursue "a number of entrepreneurial opportunities in the education field".
A spokeswoman said the moves had been timed to coincide with a restructuring by Pearson, the exam board's owners.
Pearson, the publisher of the Financial Times, controversially acquired a 75 per cent stake in Edexcel in 2003, making it the first major privatised exam board. Last month, it bought the other 25 per cent from the Edexcel Foundation, a charity.
Mr Kerr, who earned pound;219,000 in pay, pensions and bonuses in 2003, was responsible for supervising millions of exam entries every year. He did not respond to attempts by The TES to contact him.