Julio Cesar Chavez -- Call Me Grandpa! ... Junior Has Baby Girl

Legendary boxer Julio Cesar Chavez -- arguably the greatest Mexican fighter of all time -- is now officially a grandfather ... 'cause his son Julio Cesar Chavez Jr. just had a baby girl, TMZ Sports has learned.

We've obtained a birth certificate for Julia Chavez ... who was born at Cedars-Sinai Medical Center in LA yesterday afternoon to Junior and his baby mama Frida Munoz. It's Junior's first child.

FYI -- Junior is also a professional boxer and was formerly the WBC Middleweight Champion.

Million. Dollar. Baby.