It will also introduce tougher fines for rogue parking, as part of a wider overhaul of the highway code.
The Senate gave final approval to the law with a 83-47 vote.
Like in other European countries, e-scooter usage has surged in Italy in recent years. But the boom has also brought a rise in accidents and complaints from drivers and pedestrians about riders flouting safety and parking rules.
"No more wild scooters," Transport Minister Matteo Salvini said in a social media post, adding that e-scooters will also be required to have license plates and be banned from cycle lanes, pedestrian areas and non-urban roads.
National statistics institute ISTAT said in July that road accidents with injuries involving e-scooters rose to 3,365 in 2023, with 21 deaths, up from 2,929 injuries and 16 deaths in 2022.
Other countries in Europe have also restricted e-scooter use. Last year, French capital Paris banned rented two-wheeled electric vehicles following a referendum, and Madrid decided in September to ban them also.
Advocates of e-scooters, which in cities like Rome and Milan are popular with locals and tourists, say they provide a zero-pollution and cheap alternative to public transport or other mobility options.
E-scooter rental companies criticised the restrictions as overly punitive, pointing out that their vehicles are subject to speed restrictions and are geo-localised, minimising risks of misuse.
"They have a technology that inhibits certain bad behaviours that are the source of the most serious accidents," Andrea Giaretta, Vice President for Southern and Western Europe, Middle East at Dott, told Reuters.
Giorgio Cappiello, head of institutional relations in Italy for Bird, another rental company, called the new rules "completely ideological" and said his firm reported no casualties on their vehicles in 2022 and 2023.
The revised highway code also includes stiffer penalties for driving under the influence of alcohol or drugs, as well as a jail term of up to seven years for those who abandon animals on the road, leading to accidents.
Salvini, who is also deputy prime minister and leader of the hard-right League party, said the changes were drawn up after wide consultations "with a common goal: reduce the carnage on Italian roads."