Carle, who joined City from Turkish side Genclerbirligi in January, was part of the Robins side which beat Palace in the play-off semi-final last season.
"I'm very excited to be here," Carle told Palace's official website. "I know a fair bit about Palace having played against them four times last season.
"It's a massive club. I've got ambitions and after speaking to Neil Warnock my decision was easy - he sounds like a real winner."