The Brazilian joins on an initial season-long loan for a fee of €2 million.
The deal includes a compulsory purchase clause – for a further fee of €8m – should certain conditions be met before the deal ends on 30 June 2017.
The 25-year-old completed the contract formalities on Thursday after arriving at Roma's training camp in Pinzolo on Wednesday evening.
“I'm really happy to have joined such a great club and I can't wait to get started," he told Roma TV. “I can promise the fans that I'll always give my all and never stop running for Roma.”
Juan Jesus is the 41st Brazilian to don the Giallorossi jersey in the club's history – following in the footsteps of recent captures Gerson and Alisson.
After making his professional debut for Internacional in March 2010, the defender joined Inter in January 2012 and made his Serie A debut against Lazio in May that year.
He scored his first – and so far only – goal in Italy on 19 May 2013, in a 2-5 home defeat against Udinese.
In four years with the Nerazzurri the centre-back racked up 110 Serie A appearances - playing 20 times in the Europa League and on a further 12 occasions in the Coppa Italia.
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