Billy Bush's wife has filed for divorce ... TMZ has learned.
Sydney Davis filed legal docs to end their marriage, citing irreconcilable differences.
Sydney is asking for joint legal and primary physical custody of 13-year-old Lillie and 17-year-old Mary. Josie, their oldest daughter, is an adult. Billy will get visitation, according to her documents.
As for spousal support ... Sydney wants it. FYI ... in addition to other assets, Billy scored many millions in a settlement when he left "Today."