The 'Maggie May' singer, who has eight children in all, said in a statement that the day of the arrival was one of "the happiest days of his life".
Rod's daughter Kimberly gave birth to an 8lbs, 10oz girl on Sunday, in the company of her mother Alana Collins - Stewart's first wife - and the child's father Benicio Del Toro.
The 66-year-old recently told People magazine: "I'm going to be a grandfather, I've been waiting for that for so long - that and getting my bus pass - the two things I was looking forward to getting. My joy is indescribable."
Del Toro's rep originally announced the news yesterday, while in a later statement the pair said they were "thrilled" by the arrival.
Reports of Kimberly's pregnancy first emerged in April, when it was also confirmed that the pair were no longer a couple.
Watch the video for Rod Stewart's 'Time After Time' below: