The 20-year-old defender was released by the Gunners this summer following nine years at the club.
Meade has penned a one-year deal at the Liberty Stadium.
"I've been at Arsenal since I was 11, so to come to Swansea was the perfect move for me in terms of style," he told the Welsh side's official website.
"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."
Meade made his Arsenal debut in October's 7-5 victory at Reading in the Capital One Cup.