Rabbi Lionel Blue died in the early hours of Monday morning.
The BBC Radio 4 regular was made an OBE for his services to broadcasting and was a contributor to Thought for the Day for more than 25 years.
He stunned listeners when he announced he was gay.
A representative from the London synagogue, Beit Klal Yisrael, made an announcement via their Facebook page this morning.
Their statement read: “Lionel was a wonderful and inspirational man, who spoke with such wisdom and humour and whose words reached out far beyond the Jewish community.
“He was a friend and mentor to many and his courage in coming out as gay in the 1970s paved the way for many other Jews, including many Rabbis.
“We will not see his like again. May his memory be for a blessing.”
Rabbi Jonathan Romain of Maidenhead synagogue said of Rabbi Blue that he was “God’s best PR man in Britain”.
Tributes also came from Rabbi Charley Baginsky, Liberal Judaism’s director of strategy and partnerships and a student of Rabbi Blue, said he was a “pioneering rabbi, teacher and mentor.
She added: “Rabbi Lionel Blue OBE – who died in the early hours of this morning at the age of 86 – was a pioneering rabbi, teacher and mentor.
“One of Britain’s best known rabbis, he entertained the nation for decades with media appearances, his most famous being as a regular on Thought for the Day on BBC Radio 4’s Today programme.
“On a personal level, as a lecturer at Leo Baeck College, Lionel was the archetypal rabbi’s rabbi – always there for us as individuals, helping us understand our own personal and spiritual journeys.
“And he leaves a legacy like few others. As the first British rabbi publicly to come out as gay, in the 1970s, Lionel paved the way for many others, including clergy of all faiths.
“His courage and pioneering spirit have created a more equal Judaism, and a more equal world. Our thoughts are with his family and friends. May his memory be a blessing.”
Rabbi Blue read history at Balliol College, Oxford, and Semitics at the University of London before being ordained in 1960.
He was the first British rabbi to publicly affirm his sexual orientation, although he had been openly gay since the 1960s, and had lived with his partner Jim for over thirty years.