The 19-year-old has signed a permanent deal after being on trial with the Swans since the start of July.
Since his arrival at the Liberty Stadium, Vickers has played for the club’s development squad as well as producing an impressive second-half performance for Gary Monk’s first team in a pre-season friendly against 1860 Munich.
The young keeper rose through the Arsenal academy, where he spent 12 years, and will be reunited with former Gunners goalkeeping coach Tony Roberts and Lukasz Fabianski.
“I’m really pleased to have signed my contract with the club,” Vickers told the club’s official website. “I have been here five or six weeks now, taking part in some great matches and feel I have settled in well.
“It’s going to be great to work with Tony (Roberts) and Lukasz (Fabianski) again and everyone has welcomed me really well.
“Tony called and asked if I would come in on trial. 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.
“This club is going in the right direction. How the first team performed last year is breathing confidence though the whole team, it is a club on the up and its great to be a part of.
“My aim here is to push on. I hope to be training with the first team most days and to feature for the Under-21s doing the best I can, and I think there is a chance for me to grow and develop here.”