Matthew was diagnosed with leukemia in June. He applied for the pension following the advice of a staff member from Centrelink. However last Friday he was told that he did not qualify for the payment.
Centrelink admitted to mishandling of the case following "an unfortunate breakdown in communications".
Following a review Human Services Minister Joe Hockey has announced that Centrelink would grant Matthew the pension.
He said, "When I became aware of the case I requested a full review by Centrelink. Additional medical information has become apparent to Centrelink which has enabled the Disability Support Pension to be granted to Matthew."
Mr Hockey wished Matthew all the best for a speedy recovery and said he wanted to make it clear the case was not related to the welfare to work changes as the application was made prior to July 1.