Police were called after staff reported around 20 wrapped gifts were taken from the famous children's hospital in London between Friday and yesterday.
The gifts, which had been bought using the hospital's charity fund, included portable DVD players, DVDs, Nintendo DS games consoles, games and toys, and were to be given to children in the intensive care unit.
Now Celtic will replace the presents for the children.
The Parkhead club's goalkeeper Fraser Forster said: "It's really shocking that this has happened and the club is delighted to step in and replace the presents.
"Charity is such an important part of Celtic, and it's something the club wanted to do."
The presents were taken from a non-public area of the hospital, which has more than 200,000 patient visits each year.
A spokesman for Celtic said: "I'm sure everyone will have been shocked by the news that these presents were stolen from Great Ormond Street Hospital, and we are only too happy to help where we can in replacing these presents for the children.
"Great Ormond Street Hospital is renowned throughout the world for helping many, many children.
"Celtic's charitable roots have meant the club has always tried to help those most in need, and like everyone else, we are delighted to support the fantastic work the hospital does.
"Only last week our players visited Yorkhill Hospital for Sick Children in Glasgow, and they were delighted to meet the children and their families and, of course, the wonderful staff who do such great work there."
The valuable work of the hospital, known as GOSH and which celebrated its 160th anniversary this year, was highlighted during the opening ceremony of the London Olympics, when its young patients and staff took part.
Appealing for information, Inspector Neal Anderson, from the Metropolitan Police, said: "To steal presents that were supposed to be for children too sick to be at home with their families at Christmas is beyond belief."