The 66-year-old musician has been on a US road trip with girlfriend Nancy Shevell but decided to fly back to England early after his eldest daughter Mary, 38, gave birth to her third child.
A source told Britain's Daily Mirror newspaper: "Paul is over the moon and couldn't wait to jump on a plane."
"It's a very personal thing meeting a new grandchild for the first time, but he loves Nancy so much that he wanted her to be there."
"He is only expected to be here a few days to catch up with the family before he flies back to the US with Nancy."
Mary has two sons - eight-year-old Arthur and Elliot, five - with her ex-husband Alistair Donald. Her newborn son is her first child with lover Simon Aboud.
Paul's fashion-designer daughter Stella, 36, has Miller, three, Bailey, one and seven-month-old Beckett with her husband Alasdhair Willis.
