The BBC board of governors has rejected thousands of complaints made over the showing of Jerry Springer - The Opera.
The show is based around an episode of Springer's talk show
The corporation received around 55,000 complaints prior to the screening of the hit West End show, in January, and 8,000 after it had been broadcast.
But the governors' Programme Complaints committee voted by a 4-1 majority not to uphold the complaints.
They said the programme's artistic significance outweighed any offence which might have been caused.
The committee said that the offence caused to sizable numbers of viewers should not be taken lightly.
However, they added that attempts were made to minimise offence through appropriate scheduling, clear warnings as to the nature of the show, and other programmes which put the broadcast in context.
One governor, Angela Sarkis, disagreed with the decision not to uphold the complaints.
Ms Sarkis said she agreed on many points raised by the governors, particularly that the programme was well scheduled and signposted.
But she did not agree that the artistic significance outweighed the offence caused by what would have been considered literal portrayal of holy figures by many people.
The broadcast of the show caused particular offence to Christian groups for its portrayal of Jesus, Mary and God as guests on Springer's TV show.
During the show, Jesus is seen wearing a nappy and declaring himself to be "a little bit gay". The amount of expletives in the show - around 300 - also caused offence.
Stephen Green, National Director of the group Christian Voice, told BBC News he was "very disappointed" with the governors' decision.
"It's a complete abrogation of their responsibility in my view," he said.
"They have just exonerated the producers for putting on the most blasphemous thing ever to be shown on the BBC."
Earlier this month another Christian group, the Christian Institute applied for a judicial review of the broadcast.
The group said the programme breached the BBC's charter and broke the Human Rights Act by discriminating against Christians.
In response to Wednesday's decision, institute spokesman Mike Judge said: "We still feel the broadcast went against the Royal Charter and discriminated against Christians in a way they would not discriminate against any other religion."
Joel Edwards, general director of the Evangelical Alliance, said viewers would be "bewildered" by the decision.
"We are deeply disappointed that the BBC felt able to set aside the strong and sustained objections from such a volume of viewers."
A spokesman for the Church of England said they were disappointed by the outcome.
"This was a programme that gave rise to unprecedented levels of public concern and, as the governors concede, caused significant offence to large numbers of people."
However, the National Secular Society welcomed the decision.
"The BBC decided to show Jerry Springer - The Opera not because it wanted to offend people but because it adjudged it to have artistic merit," said vice-president Terry Sanderson.