The 19-year-old has been heavily linked with a move away from Stadio Olimpico this summer after a breakthrough campaign in 2012/13.
“We were awake all night trying to reach an agreement,” Luan Aoas told Lancenet. “But finally we succeeded.
“This is great news for everyone.”
Neither club have confirmed the deal, but reports have suggested that Laurent Blanc's men are set to pay the Giallorossi €32million (£27.5m) plus €3m (£2.5m) in bonuses.