Alexander Wedderburn was born in Scotland on February 13, 1733. He entered the University of Edinburgh in 1746, gained admittance to the Honourable Society of the Inner Temple in 1753, practiced on the Faculty of Advocates in Scotland beginning in 1754, worked as an advocate for the poor, helped found the Select Society, and assisted with the publication of the first Edinburgh Review. He also served in the General Assembly of the Church of Scotland as a representative from Inverkeithing (1754-1756) and Dunfermline (1756-1757). Following a quarrel with the Dean of the Faculty of Advocates Alexander Lockhart, Wedderburn quit the Scottish in favor of the English courts.
Wedderburn was called to the English Bar in 1757 and his political influence grew (partly on account of his acquaintance with John Stuart, Lord Bute). Wedderburn served in Parliament for Ayr Burghs in 1761, became king's counsel in 1763, and later traveled to London where he became active within the Court of Chancery. He married Betty Ann Dawson in December 1767, shortly before he entered Parliament for Richmond. Originally a Tory, Wedderburn gained notoriety for supporting the populism of John Wilkes in 1769 and he returned to Parliament (as a Whig) for Bishop's Castle in 1770. On December 26, 1770, Wedderburn became solicitor general and he publicly advocated a strong position against the demands of American colonists. His denunciation of Benjamin Franklin before the Privy Council in January 1774 accelerated the deterioration of Anglo-American relations. Wedderburn was appointed attorney general in June 1778. He obtained the title Baron of Loughborough and an appointment as chief justice of the Court of Common Pleas in 1780.
Alexander Wedderburn served in the Court of Common Pleas for 13 years. His position as first commissioner of the great seal under the coalition government of Lord North and Charles James Fox, April to December 1783, reflected his political prominence. Wedderburn became close to the Prince of Wales during the protracted illness of King George III and helped lead the Whig Party's opposition to the government of William Pitt. He accomplished what may be his most notable political triumph in January 1793, when he deserted the Whigs, pledged allegiance to the Tory administration of William Pitt, and received an appointment as lord chancellor. Although he held the office throughout Pitt's tenure, he was not offered a place in the new cabinet after 1801. Wedderburn received the earldom of Rosslyn and a secure pension, but continued to attend cabinet sessions until formally instructed to abstain. He died on January 2, 1805.