Veltroni, who served as Rome mayor from 2001 to 2008, will wed the pair on September 29th in the former Doge's Palace, Ca' Farsetti, Corriere della Sera reported.
Clooney and Veltroni reportedly met when the actor came to Rome to receive a Summit Peace Award for his humanitarian work in Darfur from the Nobel Peace Prize Laureates in 2007, and the pair have been close friends ever since.
In 2009, when Clooney went to the Italian capital to promote his film Leatherheads, he reportedly spoke of the former mayor in very flattering terms.
“I consider him to be a great friend, like Obama,” Clooney told reporters, according to Corriere della Sera. “Few people rarely have something very special, the ability for leadership, as well as great speaking skills, like Obama. In Veltroni I felt the same power.”
Oscar-winning Clooney announced in April that he was engaged to his then 36-year-old girlfriend.
The heartthrob US actor's spokesman confirmed the wedding venue but not the date, after Clooney let slip his plans to marry the British human rights attorney in the picture-postcard Italian city.
"I met my lovely bride-to-be here in Italy, whom I will be marrying in a couple of weeks, in Venice of all places," People magazine quoted him as saying at an awards ceremony on September 7th in Florence, Italy.
Earlier reports said they could tie the knot on an earlier date of September 26th, but the A-list actor's spokesman Stan Rosenfield played this down, telling AFP: "He did not give a specific date.
"I can only confirm that he is getting married in Venice," he said.
During the Florence award ceremony, the couple appeared very much in love, according to celebrity bible People.
Clooney put his arm around her shoulder and carefully brushed her hair back whenever her "flowing locks" fell out of place as she laughed.
News that Alamuddin had stolen 53-year-old Clooney's heart caused a global media frenzy and furious speculation about when they would wed.
They had come out as a couple last October in London, and since have been seen together in New York and on trips to Tanzania and the Seychelles.
Clooney was married to US actress Talia Balsam for four years between 1989 and 1993 but has shown little interest in settling down since, instead going through a string of younger model and actress girlfriends over the years.
Like his fiancée, he has long shown interest in human rights issues such as the humanitarian crisis in Darfur. Alamuddin worked with the international tribunal examining the assassination of former Lebanese prime minister Rafiq Hariri, and assisted ex-UN head Kofi Annan in efforts to make peace in Syria.
In August Alamuddin, who is fluent in Arabic, French and English, declined her nomination to join a commission probing Israel's Gaza offensive.
The British law firm that employs Alamuddin sang her praises when their engagement was announced.
Chief executive Robin Jackson said: "Amal has been utterly wonderful since she arrived in chambers.
"She brings a bright light to everything she is involved in, and I am so delighted at her happy news."
Alamuddin's clients have included former Ukrainian premier Yulia Tymoshenko, whose detention she challenged before the European Court of Human Rights, and WikiLeaks founder Julian Assange, during his extradition proceedings.
Leading rights lawyer Geoffrey Robertson, who worked with Amal on the Tymoshenko and Assange cases, said she was "respected and admired" by everyone at the firm.
"Amal Alamuddin is a brilliant and passionate defender of human rights who has put in the enormously hard work necessary to improving them," he said.