Schindler has signed a deal in his native Germany with FC Nurnberg, although the contract length has not been announced.
The 31-year-old - who joined the club for an undisclosed fee from German outfit TSV 1860 in the summer of 2016 - etched his name into club folklore by scoring the penalty that took the Terriers to the Premier League for the first time in 2016-17 at the expense of Reading in a tense play-off final penalty shoot-out at Wembley.
He then played an integral part in Town's survival in the following campaign in 2017-18 and went onto make 185 appearances for the club.
The central defender was a regular presence during his time at the club, but has been sidelined with a knee injury since December.
On the exit of Schindler, whose deal expired this summer, Town chairman Phil Hodgkinson commented: “I’d like to begin by thanking Chris for everything he has done at Huddersfield Town over the last five-years. He helped us achieve the unimaginable and his name will forever be written in the club’s history.
“He will always be considered among the greats at Huddersfield Town, which is down to the tremendous part he played both on and off the pitch.
“Unfortunately, we knew that there was always going to be a time where Christopher left us. This is a sad day, but this is right for both him and for the club. We wish him nothing but success in the future; he will always be a friend to this club.
“When supporters are back at the John Smith’s Stadium, Chris and his family will be invited to a game where they can have the send-off they deserve and say goodbye to the Huddersfield Town supporters.”
On signing for Nurnberg, Schindler commented on the club's website: "In the discussions with the club officials, it quickly became clear to me that everything was being done to play good and successful football in Nuremberg. I would like to contribute to that."
"I am looking forward to my new role at the club with my whole family. I have played my entire career in clubs with a long and powerful tradition and it appeals to me that I can now build on that at 1. FC Nürnberg."
Nurnberg's sports director Dieter Hecking added: "We are delighted to have won an experienced and stable central defender in Christopher, who should also take a leading position in our young team due to his mentality."