One-time student activist, cinema critic, national newspaper editor, author of nine books on everything from television to Bobby Kennedy and now, with another general election looming in less than two weeks, candidate for the deputy premiership, Mr Veltroni has the kind of intelligence, energy and enthusiasm that any political party would envy. And the man only turned 40 last July.
Not only is he young and talented, he is generally considered to be the nicest guy you could ever meet - suave, well-spoken and unpretentious, a man who would far sooner drink beers and watch a movie, or see his footballing idols, Juventus, in action, than worry about the next hurdle to jump in his meteoric career. Politics, he says, is the one activity he could happily do without.
His political opponents are so unnerved by him that the only attack they dare make is that he is too nice, that his unrelenting pleasantness (buonismo in Italian) is somehow a handicap in the cut and thrust of political life.
Actually, Mr Veltroni packs so much activity into each day that some of his friends wonder if he is really human. (One of his nicknames is Kaiser Sose, after the super-gangster character in Bryan Singer's film The Usual Suspects who controls everyone and everything without ever revealing his identity).
So quickly did he rise through the ranks of journalism that he had been editor of L'Unita, Italy's biggest party newspaper, for three years before he found time to sit his professional exams. (He passed, of course.) Even in mid-election campaign, he still churns out editorials for other newspapers and cinema reviews for a weekly television magazine.
Mr Veltroni is a proud child of the 1960s, a man who started his political life as a 14-year-old schoolboy at one of Rome's most politicised high schools, infused with the spirit of Che Guevara, the anti-Vietnam war movement and avant-garde rock music.
A militant first for the Italian Communist Party and then for its successor movement, the PDS, he was never a fan of Soviet alliances, collectivisation and the dictatorship of the proletariat; instead, in common with the party leader he idolised, Enrico Berlinguer, he was an unambiguous democrat who hoped to turn the Italian left into a broad governing coalition like the US Democratic party.
At the helm of L'Unita, a position often used in the past as a springboard for left-wing leaders, he stripped the paper of its last vestiges of ideological waffle, making it clearer and more objective than many supposedly independent Italian titles and greatly expanding its cultural section. Circulation has boomed as a result.
In politics, he came within a whisker of taking over the PDS leadership following the party's defeat in the 1994 general election. He nevertheless remains deputy to his friend and fellow journalist Massimo D'Alema, and has been instrumental in forging a broad centre-left alliance, called the Olive Tree, to fight the present election. The centrist economics professor, Romano Prodi, is leader of the Olive Tree and its candidate for prime minister, but Mr Veltroni is a crucial prop and his number two.
The one thing Mr Veltroni lacks is an international profile. But, whether you realise it or not, he may have impinged on your life already: his was the first newspaper in the world to offer cut-price videos of classic films once a week, a highly successful marketing ploy that has caught on throughout the Italian media and now adopted in England by the Independent.