"Bringing Wilfried in was a no-brainer for us," said Potters manager Mark Hughes.
"He has power, speed and very good physical attributes."
Bony, 27, only managed 15 Premier League starts for the Citizens after his £28m signing from Swansea City in January 2015.
Pep Guardiola's outfit have also farmed out goalkeeper Joe Hart to Serie A side Torino for 2016/17.