Gunner Lewis-Vale, of Highley, has the mucopolysaccharide disease, MPS Type 1 Hurler, which means his body cannot convert sugar into necessary protein.
Doctors at the Birmingham Children's Hospital believe his best chance of survival is with a stem cell transplant before his second birthday which will be later this year.
A worldwide appeal was made and a match has been found in Germany.
His mother Holly Lewis-Vale said: "We are absolutely over the moon, the news is still sinking in.
"Every time we tell someone it just makes us all so emotional.
"We can’t thank everyone enough for the support and ask everyone to follow us on Gunner's transplant journey.
"A massive thank you to both DKMS and Anthony Nolan for their help."
His family have been raising urgent funds to add more donors to a stem cell register – it costs £40 to recruit each potential donor to the register.
Last month they hit their £10,000 target with the support of well wishers who have organised sponsored activities to boost the effort.
Gunner's uncle Ben Vale, 36, of Claverley, and friend Andy Tamplin will be sitting on 9,875 seats at the Montgomery Waters Meadow Stadium, the home of Shrewsbury Town Football Club on July 1 and have already raised about £3,000.