Weiner and Huma announced the decision the same day their case was scheduled to be heard by Manhattan Supreme Court Justice Michael Katz, saying they wanted to protect their 6-year-old son from the embarrassment of a public court proceeding.
"In order to reduce any impact of these proceedings on their child, the parties have decided to reach a settlement swiftly and privately," said Abedin's attorney, Charles Miller.
Abedin filed for divorce in May and listed the case as "contested" indicating a disagreement between the two, necessitating the court appearance.
The pair could refile their divorce as "uncontested" in order to avoid a court appearance.
Weiner, 53, was sentenced to 21 months in prison in September for engaging in lewd text messages with a teenage girl.