Sean “Diddy” Combs is all checked in at his new home for the next two-and-a-half years … TMZ has learned he’s begun serving his federal prison sentence.

Law enforcement sources tell us Diddy was transferred to FCI Fort Dix in New Jersey early Thursday morning, and began the check-in process. Remember, this is the prison he requested to serve his time after Judge Arun Subramanian sentenced him to 50 months in prison.

The Federal Bureau of Prisons ultimately granted Diddy’s request.

The mogul’s legal team said Fort Dix is the best landing spot for Diddy because there he will be able to “address drug abuse issues” and “maximize family visitation and rehabilitative efforts.”

The place is low security, but Diddy’s longtime lawyer, Mark Geragos, previously told Harvey on the “2 Angry Men” podcast that Diddy will have a target on his back wherever he ends up … and concerns about sexual assaults and other violent assaults are real.

In fact, Diddy already got a taste of possible violence behind bars … his team revealed at his sentencing hearing someone already planned to shank him in jail, and his close friend claimed Diddy woke up to a knife pressed against his neck.