The challenge here could be what we want to consider a gift, and what is the appropriate context to choose from a term over another. I could not find in Spanish a term describing "The recipient of a gift - and just a gift".
Instead of using the verb ser (like in "I am gifted") you would say in Spanish
He recibido un regalo
He recibido un don
Which could be better for you context since a don is
m. Dádiva, presente o regalo.
m. Gracia especial o habilidad para hacer algo.
Which could open another possibility (that does not apply to your context) since "I am gifted" could be translated as "he recibido un regalo/don" but also as "tengo un don" (I have a special gift/talent for this).
Other "honorable mentions" for word which can imply "One who receives a gift." could be
Agasajar a alguien con atenciones, servicios o regalos.
donatario (which would apply more in a legal context)
- m. y f. Persona a quien se hace la donación.
Agraciado Even if the dictionary entries don't seem to apply, the meanings of agraciar make it possible that you say
He sido agraciado I have been granted a grace/gift
and you convey that you received "gracia divina" (divine grace) or you have been granted something (a gracia/grace), which would convey very well your message and apply to your context.