Police were called to Great Ormond Street Hospital in London on Monday after 20 wrapped presents intended for children in intensive care were stolen.
The presents, which had been bought using the hospital's charity fund, included portable DVD players, DVDs, Nintendo DS games consoles, games and toys.
They were taken from a non-public area of the hospital, which has more than 200,000 patient visits each year.
The parcels, which were in a cupboard, were taken at some point between Friday and Monday.
A spokesman for the Glasgow club said: "I'm sure everyone will have been shocked by the news that these presents were stolen from Great Ormond Street Hospital,.
"We are only too happy to help where we can in replacing these presents for the children."
Celtic goalkeeper Fraser Forster said: "It's really shocking 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."