Flower, 36, was in the final year of his two-year contract with the South Australian Cricket Association (SACA), but said his young family needed a more stable living environment.
"The past few years have been extremely turbulent for my family and playing 12 months of the year has taken its toll on me physically," Flower said in a statement.
"I do not believe that I would be giving the Redbacks (South Australia) the 100 percent they deserve from me if I continued, and I also need to give my family a stable environment in which to live."
Flower said he will continue playing for Essex in the English County championship.
The Zimbabwean is exiled from his home country following his public protest during the 2002 World Cup, when he wore a black armband to signify what he described as the death of democracy in the African nation.
Flower and his wife, Bec, have three children -- aged five, three and 18 months.
"My family and I thoroughly enjoyed our time in South Australia and although it was brief, we will cherish the memories of our stay," he said.
SACA chief executive Mike Deare said he was saddened and disappointed at Flower's decision.
"While the SACA fully understands Andy's decision not to return to South Australia, we are disappointed that he will not be a part of the Redbacks squad next season," Deare said.
"Not only will we miss a quality batsman but also a player who brought strong leadership skills to the squad."
Flower scored 4,794 Test runs for Zimbabwe in 63 matches, at an average of 51.54, with 27 half-centuries and 12 centuries.