The 20-year-old was surprisingly released by Arsenal at the end of the season, despite making his first-team debut last term.
Meade has had a number of offers and trained with Belgian side Club Brugge earlier in the summer.
However, there was always Premier League and Championship interest, and now Swansea have made their move to seal a deal.
After training with the club for a number of days, Meade has been offered terms and will give Michael Laudrup options on the left side as he can also play on the wing as well as at full-back.
Meade is believed to have agreed an initial one-year deal with an option to extend.