The Italian capital outfit have secured the services of the promising midfielder, who had reportedly attracted the interest of several clubs across Europe
The 18-year-old has signed a five-year contract with the Giallorossi after the two clubs concurred on a €700,000 (£553,000) deal.
Lucca, who has already joined up with the rest of the Roma squad at the club's pre-season training camp in Switzerland, caught the eye of several European sides after impressing in Internacional's youth sides.
He moves to the Stadio Olimpico just days after his new team also completed the signing of Corinthians defender Leandro Castan.
Roma finished in seventh position in Serie A last season, which saw the club replace Luis Enrique with Zdenek Zeman at the end of the campaign.