"A profound and indescribable joy has been delivered to my heart and to our entire family," Bolton tells PEOPLE.
This is the first grandchild for Bolton, 56, who has three daughters from a previous marriage.
The recent Dancing With the Stars contestant, who is in the middle of his One World One Love tour, admits he's still getting used to the idea of being called 'Grandpa'.
"It's so weird," he admits. "I'm going to have to figure out how to own that."