The child, born on March 28, has been named as Ava Berlin Renner, the Us magazine reported.
"Jeremy Renner and girlfriend Sonni Pacheco have confirmed that they are the parents of a 7lb daughter Ava Berlin Renner. They are beyond thrilled. Mother and daughter are doing great," said a representative of the actor.
Renner first told the baby news to actress Eva Longoria at the Golden Globes on January.