TMZ Hip Hop broke the story ... federal agents nabbed Boosie Wednesday outside the San Diego courthouse where he thought he'd just gotten great news about the gun case. According to new docs we've obtained, ATF hauled him for possession of a weapon by a felon -- essentially, the same charge San Diego dropped.

In the federal docs, they say Boosie was seen on an Instagram live feed, back on May 6, with a gun tucked into the the waistband of his red jeans. The feds say San Diego PD was watching that IG feed and mobilized officers to pull over a vehicle that had Boosie riding in the back seat.

According to the feds, right before the Mercedes SUV pulled over, the SD officer noticed movement in the back seat they believe looked like someone "attempting to conceal firearms or illegal contraband" ... in their experience.

Once the vehicle was pulled over, Boosie told the officer he didn't have any weapons, but his security did. During the search, the cop found a loaded Hellcat 9mm in the guard's bag, and also a loaded Glock 9mm on the rear passenger seat.

All 3 people ... Boosie, his guard and driver were taken into custody, and cops say they heard Boosie yell at the guard, "You told me they were in the bag."

Once cops reviewed the IG footage, they matched up the Glock with the weapon in Boosie's waistband ... and that's why they busted him. Boosie was released from Louisiana State Prison in 2014 after serving more than 4 years for drug charges.