The Portuguese shot-stopper departs having been an integral member of Wolves' Premier League side, joining back in 2018.
He joined from Sporting Lisbon after cancelling his contract in the Portuguese capital following an attack by supporters. A fee of £16m was eventually agreed between the clubs.
Patricio made more than 125 appearances for Wolves, keeping 37 clean sheets in total. He leaves for an undisclosed fee thought to total around £10m, with Bruno Lage's side set to announce his replacement this week, in the shape of Olympiakos 'keeper Jose Sa.
Patricio had been linked with a move to Serie A throughout the summer, with Jose Mourinho considering the 33-year-old a key target at the Stadio Olimpico.
The Portuguese goalkeeper thanked Wolves fans for their support online, following confirmation of his exit.
"I would like to say thank you to all Wolves fans, players and staff for your love and support since the day I joined your 'pack'." he said.
"Happy times come and go but the memories with Wolves will stay forever!"
"It's not goodbye! We will be forever connected."
Meanwhile, following Patricio's exit, former Wolves shot-stopper Carl Ikeme has urged whoever comes in, to take the number one jersey - previously left vacant by the now-Roma goalkeeper.
Patricio famously held the number 11 shirt at the club, refusing to wear number one as a sign of respect for Ikeme - who had held the number before his retirement, having battled Leukaemia whilst at Molineux.
Ikeme tweeted: "With the probability of a new keeper joining us soon it would be nice to see somebody take that No.1 Jersey".