Stephen Farrow, the 47-year-old man who was wanted for questioning in connection with the murder of Rev John Suddards, has been arrested in Folkestone in the early hours of Sunday morning.
After launching a nationwide manhunt on Saturday, the police received information on his whereabouts from a member of the public.
Officers from Avon and Somerset Police, in conjunction with Kent Police, went to an address in Black Bull Road where Farrow was arrested on suspicion of murder and taken into police custody.
A Kent Police spokesman said he was detained "without incident" and no one was injured.
Rev John Suddards, 59, was found stabbed to death at his vicarage in the South Gloucestershire town of Thornbury on Tuesday.