The 36-year-old first joined the Potters in 2012 when they were in the Premier League before moving to Sevilla in 2015.
He most recently played for Sepahan but parted ways with the Iranian team at the end of last season.
The former France international has been training with the club since last month but is not expected to be fit until the end of August.
"I have played football for some huge clubs in my career, but the best relationship I had with supporters was at Stoke City," Nzonzi said.
"I will, of course, be a different player to 10 years ago, but I know I have lots to give to the team."