mid-14c., redemcioun, "deliverance from sin," from Old French redemcion (12c.) and directly from Latin redemptionem (nominative redemptio) "a buying back or off, a releasing, a ransoming" (also "bribery"), noun of action from past-participle stem of redimere "to redeem, buy back," from red- "back" (see re-) + emere "to take, buy, gain, procure" (from PIE root *em- "to take, distribute").
The -d- is from the Old Latin habit of using red- as the form of re- before vowels, as also preserved in redact, redolent, redundant. The general sense of "release, repurchase, deliverance" is from late 15c. Commercial sense is from late 15c. Year of Redemption as "Anno Domini" is from 1510s. In the Mercian hymns, Latin redemptionem is glossed by Old English alesnisse.