TMZ is reporting that "Teem Mom" Farrah Abraham has made a deal for her sex tape that has been roumered to be floating around for the past few months?

Last time we saw Farrah she was marching into the Vivid offices with her father and daughter in tow to talk dollars and cents with porn king Steve Hirsch -- who's been interested in buying the "Teen Mom"/James Deen XXX vid from the get-go.

Even though Farrah said she was considering other offers ... sources close to the situation tell TMZ, Farrah finally inked a deal with Vivid ... for close to a million dollars.

Yes, nearly ONE MILLION DOLLARS.

Not only that, we've learned the 70-minute-long skin flick will be titled: "Farrah Superstar: Backdoor Teen Mom."

[TMZ]