Vulcano has been named assistant manager at Sunderland to Regis Le Bris.
The Italian had followed Pioli from AC Milan to Al-Nassr, while having also worked with Roberto Mancini at Inter Milan. Pioli was named Fiorentina coach last week.
Now on Wearside ahead of Sunderland's Premier League return, Vulcano told safc.com: "The first sensations are really good.
"The people here are very welcoming, and I really like the atmosphere within the club. There's a great atmosphere and weather in Portugal now. It's a great opportunity for the boys to train in such a beautiful place.
"The Premier League is a dream for every manager. It's the best league in the world. It's a huge challenge, but also a fantastic opportunity to improve, test myself, and bring my ideas to bear in an extraordinary environment."
And on Le Bris, he added: "He is one of the most intelligent coaches I have ever worked with."