Theories abound, ranging from suicide at Beachy Head to shooting himself in the head and his body fed to tigers owned by his friend John Aspinall.
Although Lord Lucan was officially declared dead by the High Court in 1999, there have been alleged sightings all over the world.
Lord Bingham, 48 — first names George Charles — says the 1999 declaration had not proved death “for all purposes” and the new law allowed for a “more complete process”.
Mrs Justice Aplin approved an application under the Presumption of Death Act, effective since 2014.
The judge declared that Lord Lucan is presumed dead on the basis that she was satisfied he had not been known to be alive for a period of at least seven years.
In a short hearing the application on behalf of the new Earl was made by his brother-in-law, Michael Bloch, QC, who said there had been many reported rumours about the missing peer but police gave none of them credence.
He told the judge: “It is pretty straightforward. The evidence is all one way.”
Mrs Justice Aplin said none of the missing Lord Lucan’s family members or closest friends had seen or heard from him or had any reason to believe he was still alive.
She agreed that the evidence all pointed in one direction. The judicial process to obtain a death certificate had been complicated at a hearing in December when Miss Rivett’s son Neil Berriman was granted permission to intervene in the case.
At that hearing Lord Bingham’s counsel Mr Bloch told the court that Mr Berriman no longer objected to the orders sought “though his concerns as to historical matters remain as sensitive as ever”.
But speaking after today’s ruling Mr Berriman, 49, said: “I think Lucan’s dead. It is fantastic and I am very pleased for Lord Bingham.”
In 2012 Lucan’s brother Hugh Bingham said he was “sure” the missing peer fled to Africa following the nanny’s murder — but then said he was unsure if his sibling was alive or dead.