Andrew was born on 20 June 1835 at Hawick, Roxburghshire, Scotland, to John Tennant and his wife Jessie née Aitken.

Tennant and James Moseley in 1904 acquired and re-established the 1,487 square miles (3,851 km2) Yardea Station in 1904 after it had been abandoned a few years earlier.

[5] Tennant was a director of the Adelaide Steamship Co. Ltd. from its inception, a justice of the peace, a Freemason, and was heavily involved in breeding, raising and racing thoroughbred horses.

[4][6] Tennant died of diabetes and senile dementia in his home, Essenside, (Moseley Street, Glenelg), on 19 July 1913, and was buried in the Brighton cemetery.

[7] Essenside was located on the northern corner of Moseley and College Streets, Glenelg, a beachside western suburb of Adelaide.

[14][15] In July 1937 an announcement appeared in The Advertiser for "a bridge party for the St Peter's Glenelg Lacrosse Club" to be held at Essenside.