1610s, "the rearing of another's child as one's own," from foster (v.) + -age.
Entries linking to fosterage
foster v.
Old English *fostrian "to supply with food, nourish, support," from fostor "food, nourishment, bringing up," from Proto-Germanic *fostra-, from extended form of PIE root *pa- "to feed."
Meaning "to bring up a child with parental care" is from c. 1200; that of "to encourage or help grow" is early 13c. of things; 1560s of feelings, ideas, etc. Old English also had the word as an adjective meaning "in the same family but not related," in fostorfæder, fostorcild, fostormodoretc. Related: Fostered; fostering.
-age
word-forming element in nouns of act, process, function, condition, from Old French and French -age, from Late Latin -aticum "belonging to, related to," originally neuter adjectival suffix, from PIE *-at- (source of Latin -atus, past participle suffix of verbs of the first conjugation) + *-(i)ko-, secondary suffix forming adjectives (see -ic).