Buchanan was born 3 November 1810 in Glasgow the son of a Scots coffee planter in Jamaica. In 1832 Alexander went from Scotland to Toronto, Canada to establish a mercantile and importing business. He returned to Scotland in 1838 and shortly after sailed for South Australia on the Welcome which arrived 3 April 1839. Shortly after he left for Sydney with a number of other men intending to overland sheep: they bought 3000 sheep for themselves and also undertook to drove a herd of 5000 sheep for Frederick Dutton. Buchanan, after several further ventures, became manager of Dutton's Anlaby station a position he held for the rest of his life. When Dutton returned to England in 1853 Buchanan was in sole charge. Under his management the original flock of 5000 was increased to 60,000.

Buchanan married twice, the first marriage being to Penelope Anne Haddrick 22 January 1848. She was born 3 January 1819 and died at Anlaby 18 December 1854. They had five children. Buchanan's second marriage was to the sister of Penelope; Cecelia Haddrick on 9 April 1857. Alexander and Cecilia had four children.

Buchanan was highly regarded and served as a magistrate in the district, He died 21 May 1865 age 54.