Robert Griffin III Officially Files for Divorce

The divorce is officially underway ... 'cause Robert Griffin III has finally filed court docs looking to end his 3 year marriage to college sweetheart Rebecca Liddicoat.

Just last month, RG3 announced he had broken things off with Liddicoat -- the mother of their 1-year-old daughter -- and had moved onto a new lady ... Florida State track star Grete Sadeiko.

But now, we've confirmed the Cleveland Browns QB has filed the paperwork seeking to formally end his marriage. He filed on Sept. 7th in Texas.

Sources connected to the former couple tell us RG3 and Liddicoat are not on good terms -- and the divorce ain't gonna be pretty.

Robert doesn't seem phased -- he already got a tattoo of his new GF's name on his arm ... and has been posting love notes and couply pics of Grete on social media.