Pennant made just two appearances for the Potters last season and spent three months of the campaign on loan with Wolves, while Whitehead played 30 times but made only 12 starts in the Premier League.
Long-serving duo Rory Delap and Mamady Sidibe, who finished the season on loan at Barnsley and Tranmere respectively, also depart with their contracts at an end, as do goalkeeper Carlo Nash, defender Matthew Upson and midfielder Matthew Lund.
"The club would like to thank all the players for their contribution during their time with us and wish them all the very best for the future," read a statement on Stoke's official website.
Stoke also confirmed a string of backroom exits, with Dave Kemp, Mark O'Connor, Adrian Pennock, Paul Maxwell, Dave Kevan and Gerry Francis leaving their roles on the coaching staff.
Mark Hughes was last month appointed as the new manager at the Britannia Stadium, succeeding Tony Pulis.