One of the two home invaders who posed as a Fed Ex worker and bound a Brooklyn family before robbing them of more than $50,000 in cash and $80,000 worth of jewelry was busted by cops Tuesday, authorities said.

The suspect, 53-year-old Santiago Mateo of the East Village, was arrested after cops were tipped off that he may have been involved in the Sept. 23 caper, a law enforcement source said.

Mateo is awaiting arraignment on robbery, burglary, criminal impersonation and unlawful imprisonment charges, authorities said.

Another suspect in the robbery is still on the loose, police said.

The brazen heist on 69th Street in Bay Ridge was captured on the family’s home surveillance system and shows Mateo allegedly enter the house by posing as a Fed Ex delivery man.

He and his accomplice then taped the hands, feet and mouths of a 36-year-old woman, her 81-year-old father and 75-year-old mother, authorities said.

The two thieves then break open the family’s safe and leave with the goods and cash and leave through the house’s back door.

The bound family sit frozen until the two men drive away, according to the video footage. After the thieves drove off, the younger woman, still bound with tape, hopped to the front door and then back to the house’s living room, the video shows.

They were rescued by a neighbor, who heard a raucous at the house while he was “futzing around” with his model train set in the backyard of his home, he told The Post after the robbery.