Areas were roped off to staff and visitors as vulnerable trees were treated with contact insecticide Deltamethrin in a bid to rid the area of the pest, currently in the second instar stage.
Kew's head of arboretum Tony Kirkham said: "It's gone really well. We have been target spraying where the pests have been recorded over the past year and I think we have more or less completed it. It is going to be a massive relief to all our staff and visitors."
Kirkham said it was the best time to spray because the caterpillars are still very small and not yet at the nest-building stage.
It is after the third instar that nest building starts and their hairs become a health issue. Kirkham said: "I think with the spraying we have done now we shouldn't have to do anything else for the rest of the year though we may have a few more small outbreaks."
Around 200 trees have been sprayed and tagged, as part of the joint effort with Kew's neighbours. Kirkham added: "Hopefully with us all working together we can eradicate it, though that might not happen within one year.
"We will carry on monitoring the trees for any activity and also monitoring the biodiversity. But we are very happy with the way that the whole operation has gone and we are happy with the activity of all our neighbours."
Exclusion zones were in place from 10 to 12 May but have been removed and the gardens are now fully open to the public.