Governor of Quebec
In October 1760 Murray was confirmed in-place as British military governor of the district of Quebec. In June 1762 he submitted an omnibus report on the state of the country in some 60 pages, inaugurating central Canada's British governance, and thereafter being confirmed the first civil governor of the new Province of Quebec on 4 October 1763.
Deploying his fluent French and care to avoid inciting rebellion, as governor he was sympathetic to the French-Canadians, favouring them over Anglo-American merchants who came in the wake of the conquest, yet remained vastly outnumbered. To the east, a previous British annexation of Acadia from France had resulted in decades of internecine sectarian conflict on the Maine frontier, until that population's traumatic deportation in the war just concluded. No evidence suggests any British interest in a larger deportation in peacetime, and neither for permanent commitment of occupation forces comparable to those historically required to impose Protestant-ascendency on a disenfranchised Catholic majority in Ireland. British and other settlers continued to prefer the warmer and wealthier American colonies, showing no foreseeable prospect subsuming French-Canadians in the eighteen century.
At Quebec under Murray the Scots-speaking arrivals, conspicuously including veterans of the Major-General's own 78th Fraser Highlanders, included many from clans of historic Jacobite loyalty, and traditions of alliance with France. Their fathers and forefathers had rebelled against the unionist Crown as recently as at Culloden a decade prior, where Murray's distant kinsman had commanded the Catholic pretender's forces against a young Wolfe. His own elder brother, Lord Elibank, was presently exiled from Britain over his foiled 1752 plot to kidnap King George II.
Murray therefore ignored mandate of a new Whig government's Royal Proclamation of 1763, and its amplifying private instructions , to establish an elected Assembly when British law excluded all Catholic populations from government. He gestured instead by seating a rare Huguenot protestant francophone on his council.. To instruction "you are to consider and report to Us, by Our Commissioners for Trade and Plantations, by what other Means the Protestant Religion may be promoted", he negotiated to substitute forbidden Papal appointment of the Bishop of Quebec by a 'superintendent' elected by local clergy, for later ratification by the Holy See. This solution successfully installed the deceased Bishop's secretary, Mgr. Jean-Olivier Briand, from 1764. Despite the Proclamation's assurance that subjects (“may confide in Our Royal Protection for the Enjoyment of the Benefit of the Laws of Our Realm of England"), he did not extend this beyond the urban anglophone arrivals, leaving the local magistrates to continue applying the popular Parisian Civil law code as before, including its independent rights of wives and equality of inheritance which limited bequests. (Anglo-American Common Law then defined a woman as property of her husband, and preferred elder-sons.) Ignoring the potential for land reform, Murray left undisturbed the 'Seigneurial' distribution of feudal farming hierarchies, excepting to discharge three Fraser officers who purchased seigneuries of their own in 1763, assimilating themselves into the old order .
Murray was promoted Major-General on 26 March 1765. Complaints of the Anglo-American merchants achieved his recall in 1766 (remaining governor in name until 1768), but his Irish deputy succeeding him, Sir Guy Carleton, was allowed to maintain Murray's successfully conciliatory approach, eventually formalized and deepened in the 1774 Quebec Act by the 1770 Tory government of Lord North. Besides confirming French Civil Law, Murray further convinced North to enact a reworded oath of allegiance avoiding any disavowal of the Papacy, and to restore direct taxation by the Catholic church, supporting its clergy but also the church-run schools and hospitals. (Both steps infuriated Protestant opinion in the southerly of the continent's 18 mainland British possessions. The Continental Congress there in the following year cited the Quebec Act among 'Intolerable Acts' justifying American independence, to include the northerly colonies by invasion of 1775.)
Murray took no steps to restrict Quebec's established urban domestic slavery. After his departure, an advertisement appeared in the 1769 'Quebec Gazette' offering a "negro woman, aged 25 years, with a mulatto male child... formerly the property of General Murray".
On his return to Great Britain he was appointed Colonel of the 13th Regiment of Foot, a post he held from 1767 to 1789.