The boy's name is Jordan and his maternal grandparents, Barry and Parchi, tell TMZ ... their daughter, Kate, used to be Flav's manager for a few years -- a period during which they had a romantic relationship.

At some point, Kate -- who no longer works for Flav -- got pregnant and had Jordan, but for a good while, we're told Flav wasn't sure the kid was his son.

However, since then ... Jordan's grandparents tell us FF submitted DNA which lined up with Jordan's. Sooo, as Maury would put it ... Flav IS the father!!!

We're told child support and a custody arrangement have been established. It also sounds like Flav is spending more QT with Jordan these days -- he's taught him how to play the drums a bit -- and he's talked to Kate about Jordan taking his family name ... Drayton.

They've already filed legal docs to make it official, and there will be a hearing later this year. Jordan is Flav's eighth child, so as he might put it ... yeahhhh little boyyyy!!!