The young goalkeeper joins up with a duo who also have strong Gunners links at the Liberty Stadium.
The 19-year-old has signed a two year deal at the Liberty Stadium after spending 12 years at Arsenal and being heavily involved in the Gunner's FA Youth Cup campaign last season.
Vickers revealed that his old goalkeeping coach from North London, Tony Roberts, who is now working as part of Garry Monk's coaching staff, invited him to the club after the youngster left Arsenal.
“Tony (Roberts) called and asked if I would come in on trial," he told the Swansea site. "I know how much knowledge he has of the game, I have worked with him the last four years and I couldn't turn down the opportunity.
“It's going to be great to work with Tony and Lukasz (Fabianski) again and everyone has welcomed me really well."
The Swans site state that Vickers had been on trial with the club since July, featuring in several development squad matches and also playing for the first team in the game with 1860 Munich.
The Gunners will hope that Vickers won't come back to haunt them like Fabianski did when Swansea went to the Emirates last season, when the Pole put in a phenomenal performance to keep a clean sheet in a 1-0 away win.
The youngster took to Twitter to celebrate his transfer shortly after it was confirmed by the club.
Swansea also brought veteran Gerhard Tremmel back to the club after he was initially released this summer, while Sweden international Kristoffer Nordfeldt had earlier been signed from Heerenveen to challenge Fabianski for a first team spot.