Since January Oliver has undergone chemotherapy, surgery, stem cell treatment and a bone marrow transplant.
Laura, 35, said he is now doing well and that he should be able to travel to New York next year to have a treatment aimed at preventing it returning.
The mum-of-two said: "The incredible support and donations not just from our friends and family but around the world has been overwhelming. We are so grateful to everyone who has helped.
"It's been a really difficult year for us and back in January Oliver's prognosis wasn't good at all. But he has battled through everything and is doing well now, he's fit and strong and even back at school. Due to that we can properly start thinking about going to America next year for further treatment, which is a huge and exciting step. It's the best Christmas present ever."