Price, who announced her pregnancy in June, gave birth to son Hudson on November 6, reports The Herald Sun.
Further details about the child were not available, with an exclusive magazine deal said to be in place for the first photos and information about the new addition.
Stone has since confirmed the birth via his own Twitter page, writing: "Lindsay and I are so excited to welcome our sweet little baby boy into the world. It feels so great to be a dad!!!!"
The couple were first reported to be dating in March 2010 after attending the Melbourne Grand Prix in Australia together.
They were forced to deny rumours that they had become engaged last year while in Northern Queensland with Oprah Winfrey last year.