Essex Chief Constable Jim Barker-McCardle said told a press conference Peter Reeve had been found dead in a Writtle churchyard.
He added: "I can confirm Peter Reeve, the man wanted for the murder of a serving police officer, was found dead, with a weapon in a Writtle churchyard and no shots were fired by the police."
The family of Pc Dibell called him a "hero" and said he had paid for his actions "in the most devastating way".
Mr Barker-McCardle said a number of lines of inquiry were being pursued as to the motive.
He added: "There must have been some sort of catalyst that prompted the scale of a tragedy of this kind."
He said a handgun had been used in the attack and Mr Reeve, who was "largely unknown to police", did not hold a firearms licence.
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