The 21-year-old centre-half's move to south Wales is believed to be for a fee of £1million.
He posted on his Twitter account: "Swansea deal complete. Very happy. Was an extremely tough decision for me to leave Arsenal, but felt time was right.
"Swansea offered me an opportunity. And I'm extremely excited to start my career here, will always be thankful to Arsenal for my education."
He added "Was the toughest decision of my life. But it is a permanent deal. And now I'm raring to go with Swansea."
Press Association Sport understands that Bartley has signed a three-year deal at the Liberty Stadium.
Bartley began his career with Bolton but made the switch to the Gunners in 2007.
He signed a new contract at the Emirates Stadium last summer and spent the season on loan at Rangers after a previous short spell at Ibrox. But he was limited to 19 appearances by a hernia problem.
He will be hoping his move to Swansea allows him the chance to gain regular first-team football having made just one appearance for Arsenal.
He becomes Michael Laudrup's fifth summer signing following the arrivals of Michu, Chico Flores, Jonathan de Guzman and Itay Schechter.