In the run-up to the US presidential election, the online magazine Slate ran a series of dictionary definitions of "Obamaisms". One ran thus: "Barocrates (buh-ROH-cruh-teez) n. An obscure Greek philosopher who pioneered a method of teaching in which sensitive topics are first posed as questions then evaded."

There were other digs at Barack Obama that alluded to ancient Greece and Rome. When he accepted the Democratic party nomination, he did so before a stagey backdrop of doric columns. Republicans said this betrayed delusions of grandeur: this was a temple out of which Obama would emerge like a self-styled Greek god. (Steve Bell also discerned a Romanness in the image, and drew Obama for this paper as a toga-ed emperor.) In fact, the resonance of those pillars was much more complicated than the Republicans would have it. They recalled the White House, which itself summoned up visual echoes of the Roman republic, on whose constitution that of the US is based. They recalled the Lincoln Memorial, before which Martin Luther King delivered his "I have a dream" speech. They recalled the building on which the Lincoln Memorial is based - the Parthenon. By drawing us symbolically to Athens, we were located at the very birthplace of democracy.

Here's the thing: to understand the next four years of American politics, you are going to need to understand something of the politics of ancient Greece and Rome.

There have been many controversial aspects to this presidential election, but one thing is uncontroversial: that Obama's skill as an orator has been one of the most important factors - perhaps the most important factor - in his victory. The sheer numbers of people who have heard him speak live set him apart from his rivals - and, indeed, recall the politics of ancient Athens, where the public speech given to ordinary voters was the motor of politics, and where the art of rhetoric matured alongside democracy.

Obama has bucked the trend of recent presidents - not excluding Bill Clinton - for dumbing down speeches. Elvin T Lim's book The Anti-Intellectual Presidency: The Decline of Presidential Rhetoric from George Washington to George W Bush, submits presidential oratory to statistical analysis. He concludes that 100 years ago speeches were pitched at college reading level. Now they are at 8th grade. Obama's speeches, by contrast, flatter their audience. His best speeches are adroit literary creations, rich, like those doric columns, with allusion, his turn of phrase consciously evoking lines by Lincoln and King, by Woody Guthrie and Sam Cooke. Though he has speechwriters, he does much of the work himself. (Jon Favreau, the 27-year-old who heads Obama's speechwriting team, has said that his job is like being "Ted Williams's batting coach.") James Wood, professor of the practice of literary criticism at Harvard, has already performed a close-reading exercise on the victory speech for the New Yorker. Can you imagine the same being done of a George Bush speech?

More than once, the adjective that has been deployed to describe Obama's oratorical skill is "Ciceronian". Cicero, the outstanding Roman politician of the late republic, was certainly the greatest orator of his time, and one of the greatest in history. A fierce defender of the republican constitution, his criticism of Mark Antony got him murdered in 43BC.

During the Roman republic (and in ancient Athens) politics was oratory. In Athens, questions such as whether or not to declare war on an enemy state were decided by the entire electorate (or however many bothered to turn up) in open debate. Oratory was the supreme political skill, on whose mastery power depended. Unsurprisingly, then, oratory was highly organised and rigorously analysed. The Greeks and Romans, in short, knew all the rhetorical tricks, and they put a name to most of them.

It turns out that Obama knows them, too. One of the best known of Cicero's techniques is his use of series of three to emphasise points: the tricolon. (The most enduring example of a Latin tricolon is not Cicero's, but Caesar's "Veni, vidi, vici" - I came, I saw, I conquered.) Obama uses tricola freely. Here's an example: "Tonight, we gather to affirm the greatness of our nation, not because of the height of our skyscrapers, or the power of our military, or the size of our economy ..." In this passage, from the 2004 Democratic convention speech, Obama is also using the technique of "praeteritio" - drawing attention to a subject by not discussing it. (He is discounting the height of America's skyscrapers etc, but in so doing reminds us of their importance.)

One of my favourites among Obama's tricks was his use of the phrase "a young preacher from Georgia", when accepting the Democratic nomination this August; he did not name Martin Luther King. The term for the technique is "antonomasia". One example from Cicero is the way he refers to Phoenix, Achilles' mentor in the Iliad, as "senior magister" - "the aged teacher". In both cases, it sets up an intimacy between speaker and audience, the flattering idea that we all know what we are talking about without need for further exposition. It humanises the character - King was just an ordinary young man, once. Referring to Georgia by name localises the reference - Obama likes to use the specifics to American place to ground the winged sweep of his rhetoric - just as in his November 4 speech: "Our campaign ... began in the backyards of Des Moines and the living rooms of Concord and the front porches of Charleston", which, of course, is also another tricolon.

Obama's favourite tricks of the trade, it appears, are the related anaphora and epiphora. Anaphora is the repetition of a phrase at the start of a sentence. Again, from November 4: "It's the answer told by lines that stretched around schools ... It's the answer spoken by young and old ... It's the answer ..." Epiphora does the same, but at the end of a sentence. From the same speech (yet another tricolon): "She lives to see them stand out and speak up and reach for the ballot. Yes we can." The phrase "Yes we can" completes the next five paragraphs.

That "Yes we can" refrain might more readily summon up the call-and-response preaching of the American church than classical rhetoric. And, of course, Obama has been influenced by his time in the congregations of powerfully effective preachers. But James Davidson, reader in ancient history at the University of Warwick, points out that preaching itself originates in ancient Greece. "The tradition of classical oratory was central to the early church, when rhetoric was one of the most important parts of education. Through sermons, the church captured the rhetorical tradition of the ancients. America has preserved that, particularly in the black church."

It is not just in the intricacies of speechifying that Obama recalls Cicero. Like Cicero, Obama is a lawyer. Like Cicero, Obama is a writer of enormous accomplishment - Dreams From My Father, Obama's first book, will surely enter the American literary canon. Like Cicero, Obama is a "novus homo" - the Latin phrase means "new man" in the sense of self-made. Like Cicero, Obama entered politics without family backing (compare Clinton) or a military record (compare John McCain). Roman tradition dictated you had both. The compensatory talent Obama shares with Cicero, says Catherine Steel, professor of classics at the University of Glasgow, is a skill at "setting up a genealogy of forebears - not biological forebears but intellectual forebears. For Cicero it was Licinius Crassus, Scipio Aemilianus and Cato the Elder. For Obama it is Lincoln, Roosevelt and King."

Steel also points out how Obama's oratory conforms to the tripartite ideal laid down by Aristotle, who stated that good rhetoric should consist of pathos, logos and ethos - emotion, argument and character. It is in the projection of ethos that Obama particularly excels. Take this resounding passage: "I am the son of a black man from Kenya and a white woman from Kansas. I was raised with the help of a white grandfather who survived a Depression to serve in Patton's army during World War II and a white grandmother who worked on a bomber assembly line at Fort Leavenworth while he was overseas. I've gone to some of the best schools in America and lived in one of the world's poorest nations." He manages to convey the sense that not only can he revive the American dream, but that he personally embodies - actually, in some sense, is - the American dream.

In English, when we use the word "rhetoric", it is generally preceded by the word "empty". Rhetoric has a bad reputation. McCain warned lest an electorate be "deceived by an eloquent but empty call for change". Waspishly, Clinton noted, "You campaign in poetry, you govern in prose." The Athenians, too, knew the dangers of a populace's being swept along by a persuasive but unscrupulous demagogue (and they invented the word). And it was the Roman politician Cato - though it could have been McCain - who said "Rem tene, verba sequentur". If you hold on to the facts, the words will follow.

Cicero was well aware of the problem. In his book On The Orator, he argues that real eloquence can be acquired only if the speaker has attained the highest state of knowledge - "otherwise what he says is just an empty and ridiculous swirl of verbiage". The true orator is one whose practice of citizenship embodies a civic ideal - whose rhetoric, far from empty, is the deliberate, rational, careful organiser of ideas and argument that propels the state forward safely and wisely. This is clearly what Obama, too, is aiming to embody: his project is to unite rhetoric, thought and action in a new politics that eschews narrow bipartisanship. Can Obama's words translate into deeds? The presidency of George Bush provided plenty of evidence that a man who has problems with his prepositions may also struggle to govern well. We can only hope that Obama's presidency proves that opposite.

• Charlotte Higgins is the author of It's All Greek To Me: From Homer to the Hippocratic Oath, How Ancient Greece Has Shaped Our World (Short Books).