Robert was born in Windsor Castle to William Wynyard, Colonel of the 5th Regiment of Foot and Equerry to King George III.

When the regiment was posted to Sydney, New South Wales, Australia, in 1844, Wynyard was sent on to New Zealand with 200 men to take part in the Flagstaff War against Hone Heke and Kawiti.

Wynyard was present at the siege of Ruapekapeka on 11 January 1846 and in recognition of services Queen Victoria appointed him to be a Companion of the Most Honourable Military Order of the Bath on 2 July 1846.

When a fire broke out in Auckland, New Zealand, in 1858, eventually destroying an entire city block, Wynyard was personally on the scene directing the men of the 58th Regiment in firefighting efforts.

Wynyard served for two periods (3 January 1854 to 6 September 1855 and 3 October 1861 to December 1861) as Administrator of the Government, in each case between the recall of one Governor and the arrival of the next.

[14]: 50  He was quickly confronted by the demands of the new Parliament that responsible government be granted immediately; on 2 June the House of Representatives passed a resolution, sponsored by Edward Gibbon Wakefield, to that effect.

On 31 August he appointed Thomas Forsaith, Jerningham Wakefield and James Macandrew to the Executive Council, but when Parliament met again it moved a motion of no confidence in the members.

Filling in between Gore Browne and Sir George Grey, he governed New Zealand for a short period with the advice of responsible Ministers, under Premier William Fox.