The British rocker and former All Saints pop star split last year (13) amid claims from U.S. journalist Liza Ghorbani that Gallagher had fathered a child with her.
In documents filed at the High Court in London, Appleton claims the Beady Eye frontman "admitted adultery to me prior to it becoming publicised in national newspapers", adding that the woman he had committed adultery with "now has a child" by him.
Appleton also insisted she found it intolerable to live with Gallagher following his confession.
In a statement confirming receipt of the divorce petition, Gallagher reportedly answered "yes" to the question of whether he had admitted adultery.
The judge granted Appleton a decree nisi, citing that Gallagher's admission of adultery and Appleton's inability to live with him any longer had broken the relationship beyond repair. A decree absolute, which will finalise their divorce, is expected to be issued in six weeks.
Gallagher has agreed to pay his ex-wife's "reasonable costs".
Gallagher and Appleton married in 2008 after dating for eight years. They have a 12-year-old son, Gene, together.