Ombudsman is one of the few official job titles that English took straight from Swedish.
Etymonline defines the word as an official appointed to investigate complaints by individuals against institutions or authorities. It says the word comes from Swedish, where it literally meant "commission man," and ties it to the justitieombudsmannen, the office that heard individuals' complaints about abuses of state power.
The Swedish word has an Old Norse relative, umboðsmaðr. Etymonline builds it from umboð, "commission," and maðr, "man." Wikipedia glosses the Old Norse word roughly as "representative," and says the related umbud meant "proxy" or "attorney," someone authorized to act for another.
Etymonline breaks umboð down further. It joins um-, "around," and boð, "command," which goes back to the Proto-Indo-European root bheudh-, "be aware, make aware." The maðr half comes from a root meaning "man."
The title is old in Scandinavia. Wikipedia says the Danish Law of Jutland used umbozman in 1241 for a royal civil servant in a hundred, a county division.
The office came later. According to Wikipedia, Charles XII of Sweden set up the Office of Supreme Ombudsman (Högste Ombudsmannen) in 1713 while in exile in the Ottoman Empire. Its job was to make sure judges and officials followed the law. In 1719 it became the Chancellor of Justice.
The modern office dates from 1809. The Swedish Riksdag established the Parliamentary Ombudsman through the Instrument of Government, as a supervisory body independent of the executive branch. The ombudsman's own office confirms this date and the 1713 office of Charles XII.
Etymonline lists English relatives of both roots. From bheudh- come beadle, bid, bode and forbid. From the root for "man" come alderman, yeoman and Norman.
The word stayed Nordic for a long time. Wikipedia notes that Denmark has ombudsmand, and that in Finland the Swedish-speaking minority uses the Swedish term while Finnish uses translations rather than the borrowed word.
English was slow to take the word. Etymonline records the first English use in 1959. Wikipedia lists modern variants including ombudsperson, ombuds and ombud.