The Italian arrived in the summer as Regis Le Bris sought to freshen up his backroom team in preparation for Sunderland's return to the Premier League.
But Vulcano is understood to have left his role by mutual consent last week. He wasn't on the bench for Sunderland's 3-0 win over Burnley in the Premier League on Monday night.
It's understood Sunderland don't plan to replace the 37-year-old Italian at this time.
Le Bris continues to be supported by assistant head coach Isidre Ramón Madir, who also arrived in the summer as well as Michael Proctor and Alessandro Barcherini.
Neil Cutler also arrived as the club's new goalkeeper coach in the summer, while James Brayne was appointed to lead the first team's set-piece coaching.
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Vulcano started out as an analyst in Italy with Inter Milan and Fiorentina, before being appointed to the role of technical coach at AC Milan. He left to move to Saudi Arabia where he worked under Stefano Pioli at Al-Nassr, overseeing a squad that included Cristiano Ronaldo.
Pioli returned to Italy to take charge of Fiorentina in the summer - he was sacked in November - and had wanted Vulcano to go with him, but the coach wanted a new challenge and was appointed by Sunderland in July.
Earlier this season, when Vulcano spoke to the media ahead of the Carabao Cup second round tie against Huddersfield, he said: "We were in touch last season, before the Championship season, but the timing wasn't the best, because I was moving to Saudi Arabia.
"We didn't match last season, and when there was the possibility this summer, I had two, three possibilities to join clubs as an assistant coach, two as a head coach. But when I felt the trust Régis, all the leadership group, the sporting director, the football ownership, they had in me, it was easy for me to choose Sunderland.
"I felt that was the right choice, and they were pushing a lot to have me here.
"With Régis there was just a common link in football, I can say. He was looking for someone talented by his side. I don't know if I'm talented enough but I hope so.
"I came here just in order to help him, the team, the club, to achieve the highest standards as I can. I'm young, but with a bit of experience in football. So, I'm trying every day to learn and try to help."
But after just six months on Wearside, he has now moved on.
Sunderland bounced back from their West Ham defeat to thump Burnley 3-0 on Monday night and climb back up to eighth in the Premier League table.
It's Arsenal next for the Black Cats, who are now on 36 points and still in with a shout of qualifying for Europe next season.
Le Bris said: “I didn’t set a limit before the season, we are still a new promoted side doing well at home, that’s fair, but we have to work hard.
“I think the connection here with our crowd and the responsibility we feel to give the best of our game and the best of our energy as well is really important.
“So keep going, we have tough challenges ahead.”