"I abducted, raped and killed Hannah Foster," Maninder Pal Singh Kohli told the New Delhi Television network.
Asked why he was confessing, Kohli, who is in police custody, said he was "tired of running".
"I want to unburden myself," he said.
Hannah, a 17-year-old student who wanted to become a doctor, was abducted near her home in Portswood, Southampton, in March last year. Her body was found two days later.
British police have issued an arrest warrant for Kohli, and are expected to seek his extradition from India.
UN staff killed
UN staff were among six people killed yesterday when a bomb exploded in a mosque where Afghans were registering for forthcoming elections yesterday.
Four of the dead were local Afghan nationals, said the US military. The mosque was located in Afghanistan's south-eastern Ghazni province. Two UN staff were badly injured.