In December the 33-time international was temporarily suspended after he arrived at the team's training complex inebriated after a players' Christmas party.
The 29-year-old departs Racing having played 166 games since making his debut in 2015, the same season in which the club won the Top 14 title.
"Racing 92 and Camille Chat have decided, by mutual consent, to end the contract between them," the six-time French champions said.
"Racing 92 wish Camille Chat the best for the remainder of his career."
Chat joined Racing as a teenager and played in three Champions Cup finals.
He made his Test debut in 2016 but last featured for his country in 2021.
"The 12 years spent at Racing 92 were more than a career," Chat said on Instagram. "They were a personal and sporting adventure without comparison."
Another Racing hooker, Janick Tarrit, was also suspended following last month's Christmas party, for failing to turn up to training.
Tarrit returned to the team last weekend.
Racing, coached by former England boss Stuart Lancaster, are struggling in the Top 14 this season and sit ninth in the table.
