Bundesliga - Kyrgiakos signs for Wolfsburg
Kyrgiakos made 30 Premier League appearances after signing from AEK Athens for £2 million in the summer of 2009.
He previously played in the Bundesliga with Eintracht Frankfurt between 2006 and 2008.
"Kyrgiakos is a player who will strengthen us immediately and can help," coach Felix Magath told the club's official webiste.
"He is experienced, knows the Bundesliga and the rhythm (of the league) and does not need time to adapt."
Kyrgiakos said: "Wolfsburg are a good club. They won the championship in 2009.
"I'm here to play and I would like to play every game. I am fit and ready, but the coach decides when and if I get to play."
Wolfsburg have also confirmed the signing of Croatian full-back Hrvoje Cale from Turkish club Trabzonspor.