Ozzimo, a member of the Democratic Party, was handed a prison term of two years and two months at the end of his fast-track trial, Ansa reported.
The four others - Francesco Ferrara, Domenico Cammisa, Salvatore Menolascina and Carmelo Parabita - were former managers at the Rome-based catering cooperative, La Cascina.
They were given sentences ranging from two years and eight months to two years and six months.
Their case involved bid-rigging related to the Cara Mineo refugee centre near Catania in Sicily. The centre is the largest of its kind in Italy.
The four were accused of collaborating with Luca Odevaine, one of the scandal's main orchestrators and the former member of the national panel of coordination for receiving refugees and asylum-seekers.
Some 40 or so other politicians, businessmen and officials are also on trial, with all implicated in rigging tenders and other corrupt schemes designed to siphon off cash destined for everything from waste recycling to the reception of newly-arrived refugees.
Gianni Alemanno, a former mayor of Rome, was also charged in December with corruption and illicit financing for his alleged role in the scandal.
Alemanno is alleged to have pocketed the €125,000 via his Nuova Italia foundation in return for “acts running counter to his duties in office”. He faces his first hearing on March 23rd.
The racketeering, which came to light in December 2014, contributed to the crumbling state of the capital's infrastructure, strained its public services and led to the downfall of mayor Ignazio Marino, who was forced out of office .
Much of the trial, which got underway in November, is expected to be taken up with arguments over whether the accused individuals can be said to have constituted a mafia-type organization as defined by legislation designed to combat more traditional crime syndicates, such as Sicily's Cosa Nostra, the Neapolitan Camorra and Calabria's 'Ndrangheta.
If the prosecution can prove that they did, the defendants will face much tougher sentences than they would if found guilty simply of corruption.