Kleber failed to make an impression on the first team at Southampton and his contract at St. Mary's has been cancelled by mutual consent.
"It was all very amicable," said Saints chairman Rupert Lowe.
"Kleber has behaved in a very professional manner. He has made a big effort to learn English and to try and force his way into the side.
"He has been unable to do that, not from a lack of ability, but because the team are playing extremely well this season and, like several other talented players, he has not been able to get in the side.
"He is a respected international and at this stage of his career he needs to be playing first-team football."