Kraft Foods Inc
Vernon is currently president of Kraft Foods North America.
The maker of Cadbury chocolate and Oscar Mayer lunch meat said it still expects to complete the split-up by the end of 2012.
Rosenfeld, 58, has been CEO of Kraft since 2006 and is credited with integrating Nabisco, leading Kraft through its spin-off from Altria and acquiring Lu biscuits and Cadbury candy. She was widely expected to lead the snack business.
Kraft also said John Cahill, currently a partner at Ripplewood Holdings, would join the company and become nonexecutive chairman of the North American grocery company.
Cahill has held senior finance positions with PepsiCo Inc
Kraft shares were down 8 cents, or 0.2 percent, at $36.42 on the New York Stock Exchange in morning trading.
(Reporting by Martinne Geller; Editing by Derek Caney)