After his arrest, Kangethe fled from a Kenyan police station and is now wanted.
The family of Kangethe's girlfriend, Margaret Mbitu, told US media that he had planned to end their relationship before he was killed. Margaret was a 30-year-old Kenyan-American nurse working in Halifax, Massachusetts.
Margaret was last seen alive on the evening of October 30 last year as she left her workplace. She was reported missing the same day and her body was found two days later.
Authorities said they believe Kangethe left the US immediately after committing the murder. Security footage showed Margaret's body was found in an airport parking lot.
A Kenyan court will decide how Kangethe, who renounced his US citizenship last year, will be found and tried in Kenya and whether he should be extradited to face first-degree murder charges in the US.