The Take That star is thrilled for his bandmate after his wife Ayda Field gave birth to their daughter Theodora Rose yesterday (18.09.12).
Gary - whose fourth child Poppy was tragically delivered stillborn last month - tweeted: ''Massive congrats Rob and Ayda. So happy for you.''
Robbie's best friend Jonathan Wilkes also took to twitter to express his delight at the new arrival.
He wrote: ''Just had the best news!''
It is believed Ayda went into labour eight days early, with the baby - who will be known as Teddy - born at London's Portland Hospital at 3.33pm and Robbie was present for the delivery. She weighed 7lb 4oz.
A source told The Sun newspaper: ''Robbie was at Ayda's side throughout - she did so well. They spent their first night together as a happy family.''
Announcing the news on his official website, a delighted Robbie said: ''Baby, Mummy and Daddy are all rockin'.''
The 38-year-old singer and 33-year-old Ayda began dating in 2006 and married in August 2010.