Lord Janner has died at the age of 87.
In a statement, his family said: "Lord Janner died peacefully on Saturday, 19th December after a long illness.
"He will be deeply missed."
A former Board of Deputies president, from 1978-84, and long-serving MP, Lord Janner was a leading figure in Anglo-Jewry for more than 40 years.
Following the announcement of the peer's death, Sir Mick Davis, chairman of the Jewish Leadership Council said: "The passing of Greville Janner marks the end of an era for the Jewish community, our thoughts and prayers are with the Janner family at this most difficult time."
A Board of Deputies spokesperson said: "Following the passing of Greville Janner after a long illness, our thoughts and prayers go out to the whole Janner family."
Greville Janner QC, Lord Janner of Braunstone, was Labour MP for Leicester West for 27 years before stepping down in 1997. The father-of-three was founding patron and chair of the Holocaust Education Trust and served as a vice president of the World Jewish Congress.
He held a number of leading positions on groups serving world Jewry.
Karen Pollock, chief executive of the Holocaust Educational Trust said: "In 1988 Greville Janner had the foresight to know we as a nation needed to know about and remember the Holocaust and so established the Holocaust Educational Trust. Our thoughts are with his family at this difficult time."
Lord Mendelsohn, president of the Commonwealth Jewish Council, said: "Greville's contribution to Commonwealth Jewry will be long remembered. Our thoughts and prayers are with the family".
Yiftah Curiel, spokesman of the Israeli embassy, tweeted: "The Embassy of Israel in London is saddened to hear about the death of Lord Greville Janner. Our thoughts and prayers are with his family".
Veteran Soviet Jewish leader Natan Sharansky described Lord Janner as a comrade-in-arms.
In a letter reportedly sent to Lord Janner’s family, Mr Sharansky, now chair of the Jewish Agency, praised the peer’s support for the campaign to highlight the plight of Soviet Jews in the 1970s
Lord Janner was a former president of the National Council for Soviet Jewry.
An ongoing legal case had been investigating claims against him relating to historic child abuse, but a series of judges had ruled he was not fit to stand trial.
A "trial of the facts" was due to take place in April 2016, which would allow a jury to decide whether he had committed the offences, but there would be no finding of guilt or a conviction.
His family had repeatedly said he was not guilty of any wrongdoing.
Lord Janner was born on July 11, 1928 in Cardiff, the son of MP and Anglo-Jewish leader Barnett Janner.
He attended St Paul’s School in London, and Trinity Hall, Cambridge, becoming president of the Cambridge Union, and later won a Fulbright scholarship to study at Harvard Law School.
He became a barrister in 1954 and was appointed Queen’s Counsel in 1971.
As a Labour MP, he followed his father in representing Leicester North West, winning the seat in 1970.
He held it in 1974 when it was renamed Leicester West.
