The 21-year-old made just one senior appearance in five years for the Gunners and joins Michael Laudrup's side on a three-year deal.
Swansea have not revealed the fee paid for Bartley, who played in the Clydesdale Bank Scottish Premier League last season on loan at Rangers while he has also had two spells at Sheffield United.
Bartley could make his Swans debut against QPR at Loftus Road on Saturday, subject to receiving international clearance.
Speaking to Swansea's official website he said: "I spoke to Arsene Wenger briefly last week and he said that my game-time would be at a minimum.
"For that reason, I wanted to at least go out on loan but when Swansea came in for me it was too good an opportunity to turn down."
Bartley cites Swansea's style of play and new manager Laudrup as the attraction of signing for Swansea.
"I do like to play football and play the game from the back, which is exactly how Swansea want to play, and that was a massive factor for me," he added.
"We showed last year that we can compete, we've got another great manager in Michael Laudrup and we're hoping that we can achieve the same things."