The detective leading the inquiry, DCI Simon Crisp, told ITV West that Stephen Farrow would have murdered more people if he hadn't been caught.
The Rev John Suddards' sister Hillary Bosworth read a prepared statement outside court.
The Judge, Mr Justice Field, said Farrow should spend the rest of his life behind bars.
The sister of the Rev John Suddards has welcomed Stephen Farrow's conviction for murder. Hilary Bosworth told reporters outside court that the verdict was a just one which reflected the gravity of the situation.
She also praised the brilliance of the police detective work which led to Farrow being caught within 6 days.
The Bishop of Gloucester, the Rt Revd Michael Perham and the Bishop of Tewkesbury, the Rt Revd John Went, issued a joint statement after the conviction and sentencing of Stephen farrow.
The murder of the Rev John Suddards by Stephen Farrow devastated the close-knit community of Thornbury. Richard Payne reports on the impact on the quiet South Gloucestershire town.
Stephen Farrow, 48, who was convicted of the murders of the Rev John Suddards from Thornbury and retired teacher Betty Yates, was today told he would spend the rest of his life in prison by a judge at Bristol Crown Court
A homeless drifter was convicted today of the brutal murders of a Thornbury vicar and a retired teacher in their homes.
Stephen Farrow, 48, was found guilty of killing the Rev John Suddards, 59, and Betty Yates, 77, by a jury at Bristol Crown Court.
Farrow, who was diagnosed as a psychopath, denied the murders of Mr Suddards and Mrs Yates.
But Farrow, of no fixed abode, admitted the clergyman's manslaughter on the grounds of diminished responsibility, and a separate burglary.
Farrow had an obsession with religion - claiming he had been sexually abused at boarding school by a priest - and wanted to murder the Archbishop of Canterbury.
The murder of Mr Suddards at his vicarage in Thornbury, South Gloucestershire, was the culmination of a two-month reign of terror in which Farrow killed Mrs Yates and threatened to kill "Christian scum".
Stephen Farrow, 48, has been convicted of the murders of the Rev John Suddards in Thornbury, South Gloucestershire, and retired teacher Betty Yates, in Bewdley, Worcestershire, by a jury at Bristol Crown Court.
Jurors in the trial of a homeless drifter accused of the murders of a vicar in South Gloucestershire and a retired teacher in Worcestershire will resume their deliberations this morning.
Stephen Farrow admits the manslaughter of Rev John Suddards but denies murdering the clergyman between February 12 and 15 this year on the grounds of diminished responsibility.
His also denies the murder of Betty Yates between January 1 and 5 this year. Both victims were found stabbed in their homes.