The 29-year-old will stay in the Premier League despite suffering relegation with the Swans last season
The 29-year-old has signed a two-year deal and will join on a free transfer when his contract expires.
“I’m so pleased I can join the club,” Ki said on the Newcastle’s official website. “I was always pleasantly surprised when I came to St James’ Park to play against Newcastle – there is a great atmosphere and the passion from the fans is a great support to the players.
“Everyone knows how big this club is so I’m really looking forward to playing with my teammates and for the fans.”
Newcastle announced the move on Friday, with the midfielder following Martin Dubravka into St James’ Park this summer.
“I’m pleased to welcome Ki to the club. He is a player with lots of Premier League and international experience and it was an easy decision to bring him here,” United boss Rafael Benitez said.
“He is the captain of his country, a good character and he will be a good addition to the squad.”
Ki started out with FC Seoul but is well known to British fans, having joined Celtic in 2009.
He spent three seasons with the Bhoys before starting a six-year spell with Swansea that was punctuated only by his loan spell at Sunderland in 2013/14.