Michael Young, nine, and his family met Nicola Sturgeon in June after the Scottish Medicines Consortium (SMC) refused to approve Translarna to treat the muscle-wasting condition Duchenne muscular dystrophy.
The SMC said in April there was too much uncertainty about the overall benefits in relation to its cost.
The family organised an online petition calling for a rethink of the decision which received the backing of more than 150,000 people.
A personal letter from Ms Sturgeon confirmed Michael and five other boys eligible for the drug will receive it through the individual patient treatment request agreement.
Most boys with Duchenne will be in wheelchairs by their 12th birthday and few live beyond their late 20s, the charity Muscular Dystrophy UK said.
It is hoped Translarna could keep eligible boys walking for longer while also maintaining the prospect of accessing potential treatments of the future.
Michael’s mother Michelle said: “To have our lovely, quiet boy rewarded for all his brave and tireless campaigning was just amazing; for him and our family.
“Knowing that we no longer have to worry about Michael receiving his medication is a tremendous relief. Any extra time Michael spends on his feet is just invaluable.
“We are profoundly thankful for the time Nicola Sturgeon spent with us. To receive this letter from her was just a wonderful surprise and a much-needed lifeline.
“It’s so special knowing Michael will be given vital medicine and can just get on with enjoying his childhood again.”
While the SMC rejected the drug earlier this year, it was approved for funding by Nice, the equivalent body in England.
The drug is also available in some European countries, including France and Germany.
Robert Meadowcroft, chief executive of Muscular Dystrophy UK said: “Michael and his family have displayed such incredible determination, commitment and patience with his dedicated campaign.
“To receive this surprise letter from the First Minister is an absolutely well-deserved end to our battle to access Translarna.
“We would like to say a big thank you to Nicola Sturgeon, who has been focused and engaged throughout this campaign.
“It is entirely admirable that she twice met with the Youngs and our charity to hear our concerns.”