Their son Robin-John and his wife Megan announced the arrival of their second baby, a little boy named Theodore-Alexander Hugh Gibb.
In a statement Mrs Gibb said: "Even though it is a joyful occasion, it is sad that Robin is not here with me to share in the happiness of seeing our grandchildren flourish and grow. I am glad they will have the music."
Robin-John Gibb said: "I know that my father would have been a wonderful grandparent because he was such a loving, attentive and inspirational father.
"We miss him terribly and it is sad to know that had he lived just a little longer, he would have met his two grandsons: Maxwell and Theodore.
"Although they will never meet him, it is great that they will always hear his voice."
Robin Gibb died in May 2012 after contracting pneumonia while battling colon and liver cancer.
As well as two children from his first marriage to Molly Hullis, Spencer (41) and Melissa (39), he had one child with Dwina, Robin-John (28).
He left his Northern Ireland-born widow and three children a Porsche, a yacht, and a stone mansion in New Jersey - just part of a £26m fortune bequeathed to his family.
Dwina was married to Gibb for 28 years.
Before the birth of her first grandchild, she told Hello! Magazine in early 2013 that New Year without her husband had been difficult, saying: "I'd spent every New Year's Eve of our 32 years together with Robin and missed him desperately."
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