Lawyer David Becker, acting on behalf of the couple, told media: "I confirm that Graeme and Morgan are unfortunately divorcing. This is obviously a private matter and the couple would ask that their privacy is respected during this time, both for the sake of themselves and their children."
Smith, 34, played 117 Tests for South Africa before retiring in 2014, citing family commitments.
Somewhat infamously, Smith went straight to Ireland to meet his then girlfriend Deane after the Proteas choked at the World Cup final in India in 2011.
The couple have a daughter, Cadence Christine Smith, 3, and a son, Carter McMorrin Smith, who is a year-and-a-half old.