The left-back, who was a free agent after leaving Arsenal earlier this summer, will initially work within Kristian O'Leary's U21 set-up.
But his longer-term aim is to challenge Ben Davies and Neil Taylor for a place in Michael Laudrup's first-team squad.
"I've been at Arsenal since I was 11, so to come to Swansea was the perfect move for me in terms of style," Meade told the Swansea 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.
"My aim is to start impressing in the U21 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.
"And he 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."
Meade appeared twice for Arsenal's first team last season, earning a first start at Olympiakos in the Champions League.