Sean Lopes was nabbed Monday on Victoria Road after a member of the public raised concerns.
Kent police detectives contacted the NYPD and the Metropolitan Police, and the suspect was arrested.
Lopes appeared at Westminster Magistrates' Court Tuesday and was remanded until May 14.
U.S. authorities said last year that they believed Guyanese-born Lopes was hiding in Trinidad and Tobago, describing him as a violent fugitive.
In 2004, apparently furious that she had dumped him, Lopes allegedly snuck into the 22-year-old Bronx teacher's apartment on the last day of school. Stashed in his duffel bag were a pair of black gloves, a black ski mask, a BB gun made to look like a 9-mm handgun, a stun gun and a serrated knife.
Police say Lopes tackled Hopkins when she arrived home, choked her and threatened her with the gun. For the next 40 minutes, he terrorized Hopkins - the niece of a federal magistrate in Florida - and threatened to kill her and then commit suicide. Neighbors heard Hopkins' screams and called the police.
The NYPD hostage negotiating team stormed the apartment, and found Lopes holding a butcher knife to Hopkins' throat. A K-9 dog charged at Lopes and wrestled him to the ground, allowing cops to take him into custody.
He told police a wild tale that Hopkins had been holding him hostage, saying she had overpowered him because she is taller than him.
Lopes, an eighth-grade science teacher, was charged with attempted murder and attempted kidnapping. His wife put up the family's house to free him on $250,000 bail.
Lopes jumped bail November 16, 2004. He was convicted in absentia in 2005 and sentenced to 15 years in prison.