The officers are keeping vigil at the site between 9am and midnight each day until mid-October as part of a trial run of Mayor Virginia Raggi's plan to protect the 18th century monument and others across the capital.
Anyone caught even putting their feet into the water or picnicking on the fountain's steps could face fines of up to €240.
If the officers manage to keep unruly behaviour in check during the test period, the plan will be rolled out permanently.
The move comes after a man was fined in April for taking a nude dip in the fountain. He initially tried to pass himself off as a foreigner before police established he was Italian.
But for the most part the trespassers are tourists, often in an attempt to recreate a scene from Federico Fellini's 1960 film 'La Dolce Vita' in which the late Swedish actress Anita Ekberg jumps into the Trevi.
Last July, an Ekberg wannabe was dragged out of the fountain by police, just days after three bikini-clad tourists were photographed splashing around in the water. Unperturbed, the same woman, Delilah Jay, a former model who lives in the UK, repeated the enactment earlier this month.
The fountain, commissioned by Pope Clement XII in 1730, is the end point of one of the aqueducts that supplied ancient Rome with water and was last restored 23 years ago.
The Acqua Vergine runs for a total of 20 kilometres and ends up in the fountain, where tourists can drink it from a special tap tucked away at one side of the monu-ment.
Legend has it the water source was discovered in 19BC by thirsty Roman soldiers guided to the site by a young virgin - hence the name, Virgin Waters.