The agreement came Friday during a meeting with Aubry, Berry and the Los Angeles County Department of Children and Family Services.
"Gabriel has a little bit of a temper, but the good news is that he realizes it," a law enforcement source told TMZ.com.
Authorities were called in after Berry's nanny claimed Aubry shoved her while she was holding the couple's baby. Sources told TMZ Aubry denied the allegation and it was unlikely there was enough evidence to warrant a criminal charge.
Sources said the agency was not recommending any changes to the current child-custody arrangements; however, the matter will go before a judge Monday.