The peer had been accused of 22 counts of sex offences against boys, over a 20-year period from the 1960s - allegations his family denied.
A jury was to be asked to decide - without resolving whether he was guilty - if the incidents had taken place.
A lawyer for some of the alleged victims said they were "devastated".
Meanwhile, 12 former residents of children's homes have told the BBC they were abused by Lord Janner.
Lord Janner, who had been suffering from dementia, died in December aged 87.
A trial of the facts had been due to be held in April 2016 - however, prosecutor Richard Whittam QC said on Friday that the law provided no circumstances whereby a dead defendant could face a trial, even a trial of the facts.
BBC home affairs correspondent Tom Symonds says it is expected that Lord Janner's case will now be considered by the independent inquiry into child sexual abuse led by Justice Lowell Goddard.
Mr Whittam told trial judge Mr Justice Openshaw that the Crown would not go ahead with the planned trial of facts.
Mr Justice Openshaw said: "There is nothing more to be said. That's the end of the proceedings, that the defendant is dead."
The allegations centred on claims that Lord Janner, when he was MP for Leicester West, befriended the manager of a children's care home to allow him access to children and carry out serious sexual offences.
Leicestershire Police said an investigation into allegations not just against Lord Janner but against other individuals is "live and will continue".
Liz Dux, specialist abuse lawyer at Slater and Gordon, who represents six of Lord Janner's alleged victims, said: "My clients are obviously devastated that they are no longer able to give their evidence in a criminal court.
"They understand the reasons why but that doesn't make up for the real travesty - that many gave their statements decades ago and have been denied justice through a failure to prosecute earlier when Janner was alive and well."
Her clients "sincerely hope" the Goddard Inquiry will make their cases a priority and allow them to give evidence in person, she added.
Criminal proceedings against the late Labour peer Lord Janner over sex abuse charges have ended because of his death, an Old Bailey judge has said.