Writing in The Daily Telegraph, the mayor of London hit out at the BBC's "puerile and absurd" decision to use modern phrases "Common Era" (BC) and "Before Common Era" (BCE) rather than "Anno Domini" and "Before Christ".
Johnson said that the BBC's position as a state-funded broadcaster means that the public should be consulted before it "makes a decision of immense cultural importance, a decision that affects the way we will ask our children to think about the history of our civilisation".
He accepted that there is "perplexity" around the actual date of Christ's birth, while "there will always be some who doubt that Jesus of Nazareth ever existed".
However, Johnson added: "It now turns out that some BBC committee or hierarch has decided that this nativity – notional or otherwise - can no longer be referred to by our state-funded broadcaster, in identifying whether a year is before or after the, ahem, cough, event in question.
"We are asked to call the years-before-the-event-we-cannot-mention BCE, or "Before Common Era", and the years-after-the-event-we-cannot-mention "Common Era", or CE. You should not underestimate the influence of this verdict.
"What the BBC decides, all kinds of other publishers and broadcasters will decide to follow. Schools will snap into line, and if people protest they will be told that they are following best practice - it's what the BBC does, after all. "
The beginning of the so-called "Common Era" is dated from the same point as the Gregorian Christian calendar, but removes any mention of the birth of Jesus.
BC and BCE have already gained acceptance within the BBC, with shows such as University Challenge and Radio 4's In Our Time among those to have used the terms.
Johnson, who fronted a programme on the Roman Empire for the broadcaster, said: "The BBC needs to stop spending time and money on this sort of footling political correctness. Someone needs to get out down the corridor and find the individual who passed this edict and give him or her a figurative kick in the pants.
"I know it sounds like a trivial thing to get worked up about, but one trivial thing leads to another. I urge all readers to get out their Basildon Bond and hit the emails - to [BBC director general] Mark Thompson and [BBC chairman] Lord Patten. Let's fight this Beeb drivel now."
The BBC's religious and ethics department said in a statement: "As the BBC is committed to impartiality it is appropriate that we use terms that do not offend or alienate non-Christians. In line with modern practice, BCE/CE (Before Common Era/Common Era) are used as a religiously neutral alternative to BC/AD."
A spokeswoman for the corporation added that individual BBC programmes are free to choose which terms are used. Andrew Marr said on his BBC One show yesterday that he will continue to use the traditional date descriptions.
The BBC has often attracted criticism for its religious coverage, including the leader of the Roman Catholic Church in Scotland claiming in September 2010 that the corporation was guilty of "institutional bias" against Christianity.
Earlier that year, the Church of England expressed concern that the BBC was "losing sight of its essence" to the detriment of religious broadcasting.