"I was fortunate to work with excellent people since arriving at the club," said Buckingham, "and the support provided during my three years from staff, players and fans is hugely appreciated.
"From coaching under Ernie Merrick to working closely with Chris Greenacre, my time living in New Zealand and working in the Hyundai A-League will be fondly remembered.
"Change brings opportunity and I'm excited to continue working with talented players and excellent coaches in a first-class environment at Stoke City FC.
"I wish Darije, the players and the club all the best for the upcoming season."
For General Manager David Dome Buckingham's departure comes with mixed feelings.
"It was only a few years ago that [Phoenix] goalkeeping coach Jonathan Gould took up an amazing opportunity at West Bromwich Albion," said Dome, "so to see Des also working inside a Premier League club now is another feather in our cap."
"Obviously there's a tinge of sadness seeing Des move on - we've always said that in him and Chris we've got two of the most promising young coaches in the A-League, but this move will only further enhance his reputation."