Meade, 20, came through the youth ranks at Arsenal and started in the Champions League group game away to Olympiacos in December 2012, before leaving the Emirates Stadium in the summer at the end of his contract.
The defender, who has signed a one-year deal at the Liberty Stadium, will initially train with the under-21s as he looks to force his way into contention for Michael Laudrup's first-team plans.
"I have been at Arsenal since I was 11, so to come to Swansea was the perfect move for me in terms of style," Meade said on the club's official website, www.swanseacity.net.
"Swansea are a growing club and they've come from League Two by passing their way out of the divisions.
"I think everyone has been very impressed by what they have achieved in the Premier League, and it's great to be a part of the club.
"The people in the area are very welcoming and I know it's a family club too, which is great.
"My aim is to start impressing in the Under-21s team and hopefully give Michael Laudrup another option at left-back for the first team.
"He was a great player and the chance to learn from him is a massive opportunity for me.
"The manager is not afraid to give youngsters a chance to prove themselves either. You only have to look at what Ben Davies achieved last season to realise that."
Swansea, who will compete in Europe next season following their Capital One Cup victory at Wembley, last week confirmed the signing of Ivory Coast international forward Wilfried Bony for a club-record £12million from Dutch side Vitesse Arnhem, to further bolster the squad following the arrival of Alejandro Pozuelo and Jonjo Shelvey.