"He had been unwell for some time. It's been a difficult time for Jack losing his father before the Christening."
George's cause of death is not known at this time.
Eugenie, 31, and former bar manager Jack, 35, are yet to publicly comment on the heartbreaking news.
Meanwhile, the Queen was in attendance at the rare double christening.
The appearance at the family event came after Her Majesty was forced to pull out of her Remembrance Sunday duties at the Cenotaph last weekend, due to a back sprain.
It was reported that the queen was determined to make the special occasion.
A royal source had said: "Her Majesty is very keen to be there as she knows how important this is for her grandchildren and great-grandchildren. It's set to be a heart-warming family occasion and a time of real celebration after what has been some challenging times for certain royals of late, including the Queen herself. She is keen to attend such a wonderful event after the great personal disappointment of missing last Sunday's Remembrance events."
Before the christening, the Queen - whose husband Prince Philip died earlier this year aged 99 - carried out an in-person engagement with General Sir Nick Carter, the chief of the defence staff at Windsor Castle last week, her first since October 19.
And earlier this week, her eldest son, 73-year-old Prince Charles, insisted his mother was feeling "all right", while carrying out an engagement during his and wife Camilla, Duchess of Cornwall's tour of Jordan.
He said: "She's alright thank you very much. Once you get to 95 it's not quite as easy as it used to be. It's bad enough at 73."
