Wedderburn of Blackness, Forfarshire, eldest son of James Wedderburn, town clerk of Dundee, by Margaret, daughter of James Goldman, also a Dundee merchant, was born in 1610.
Alexander was educated for the law and passed advocate; but upon the death of his uncle Alexander of Kingennie, whose son was then a minor, he was in 1633 appointed town clerk of Dundee, and held the office till 1675.
For his steadfast loyalty he obtained from Charles I in 1639 a tack of the customs of Dundee, and in 1640 a pension of 100l.
In September of the same year he was appointed one of the eight Scots commissioners to arrange the treaty of Ripon.
At the Restoration in 1661 he was appointed one of the commissioners for regulating weights and measures; and on 10 February 1664 he received from Charles II a pension of 100l.