Twenty-seven year old Taylor was the bluebird's captain during their promotion campaign to the top flight, but fell out of favour during their year in the Premiership.
Following on from the permanent capture of Martyn Waghorn, Taylor has joined the Latics on a bosman-style free transfer.
Rosler told his club’s official website: “I’m very, very happy to get a player of Andrew’s stature and experience to our football club.
“He was the captain of Malky Mackay’s promotion-winning team, he is a very experienced and reliable player who is at the best stage of his career and I’m looking forward to working with him.
“He has all the qualities in his position that we are looking for; physically, technically he’s very good and tactically he has developed as a player well.”
Taylor said: “Wigan Athletic are a big club, with Premier League experience and big aspirations.
“The manager seems really good and I think his record when he came to the club last season speaks volumes.
“It’s a fresh challenge for me and one I’m very excited about; I had three good years at Cardiff but everything has to come to an end and I’m looking forward to getting started at the DW Stadium.”
Taylor started his career in the North East with Middlesbrough where he made 125 appearances before loan spells with Watford and Bradford City.
He then moved to Cardiff City where he has made 100 appearances in the Welsh capital.
Taylor also has international pedigree and has represented England at all levels from Under 16's through to the Under 21's. He made thirteen appearances in total for the Under 21's.