The Turkey international arrived at Parkhead on transfer deadline day on 1 February on a two-and-a-half-year deal.
But after just two goals in 13 games under former boss Ronny Deila, the 29-year-old was deemed surplus to requirements by Brendan Rodgers.
"Everyone at the club wishes him the very best for the future," Celtic tweeted.
London-born Kazim-Richards, who has a Brazilian wife, has played for clubs in six countries prior to his move to Brazil. He has signed an 18-month contract with Coritiba.
His departure follows that of Anthony Stokes, with Celtic declining to take up the option of another year on the contract of the striker, who spent the second half of last season on loan at Hibernian.
Celtic have confirmed striker Colin Kazim-Richards has left the club to join Brazilian side Coritiba.