Old English glædlice "joyfully, kindly, willingly" (also "bright, shining; pleasant, agreeable"); see glad (adj.) + -ly (2).
Entries linking to gladly
glad adj.
Old English glæd "bright, shining, gleaming; joyous; pleasant, gracious" (also as a noun, "joy, gladness"), from Proto-Germanic *gladaz (source also of Old Norse glaðr "smooth, bright, glad," Danish glad "glad, joyful," Old Saxon gladmod, in which the element means "glad," Old Frisian gled "smooth," Dutch glad "slippery," German glatt "smooth"), from PIE root *ghel- (2) "to shine." Apparently the notion is of being radiant with joy; the modern sense "feeling pleasure or satisfaction" is much weakened. Slang glad rags "one's best clothes" first recorded 1902.
-ly 2
common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).
Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.