Police were called to St Richard’s Church on Kentmere Avenue in Seacroft on Saturday, where the presents were previously being stored, after the theft took place there.
Mother-of-three Sammi Abbott, 30, has organised the distribution of gifts but was “devastated” and ready to give up after what happened.
However, she said that following an appeal on social media, friends and “complete strangers” came out to donate new toys, teddies, puzzles, board games, chocolate and more.
She said: “What wasn’t stolen was vandalised.
“There was quite a lot of damage.
“The way everyone has rallied round is absolutely amazing. I’ve really not seen it first hand like I have today.
“In the room now there must be 60 bags, if not more, with all sorts of different things. There’s been some cash. It’s overwhelming.”
Mrs Abbott, who works at the LS14 Trust, added: “On Saturday night I said ‘I’m not doing it anymore’. My mum said, ‘I’ll fix this, I’ll help’.
“I just want to thank everybody for doing this.”
More than 6,000 toys and other gifts have already been distributed for babies, children and teenagers through a referrals scheme alongside St George’s Crypt.
But 600 more were due to be delivered this week, according to Mrs Abbott’s mother Tracey Parkinson.
She said: “There will probably be £2,000 worth of stuff taken or destroyed.”
“Sammi gives up her Saturday night and she cooks for the vulnerable and she’s got three kids at home. People rely on her now to do the things does.
“She just does it because she wants to help.”
The volunteer also arranges for children in need to go on coach trips in her spare time, sometimes paying for it herself.
Police confirmed that a report of theft and damage was logged on Saturday, happening at the church between 3.30pm and 6pm.
Enquiries are on going, and anyone who has information which could help officers with their investigation is asked to call 101.
When passing on information, quote the reference number 13170587729.