Police learned the first name of the 28-year-old suspect when he went to Brady's building to see her and entered it into the visitor's log.
They did a social media search using the name, Lanre, and found a YouTube clip showing a person that matched the individual seen on surveillance cameras at Brady's building.
The YouTube clip apparently lists both the suspect's first and last name, and police were able to use that information to track him to the Brooklyn homeless shelter.
Lanre Orimabogunje was apprehended at the shelter and charged with stalking. Police sources say detectives found a photo of Brady in his pocket when they arrested him.
Information on an attorney for Orimabogunje wasn't immediately available.