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."