Abby Elliott's closing two big chapters in her life ... "The Bear" and her nearly 10-year marriage to husband Bill Kennedy.

TMZ obtained a copy of the divorce docs she filed Friday, and she says she’s splitting from the producer because of irreconcilable differences. She lists the date of separation as July 8.

She wants joint legal and physical custody of their 2 minor children -- 5-year-old Edith and 3-year-old William.

Abby’s requesting spousal support and asking to terminate the court’s ability to award him any. The actress is also asking the court to have him foot the bill for her attorney’s fees.

The exes tied the knot almost a decade ago … they said “I do” on September 3, 2016.