Born in Christchurch on 24 April 1940, Robinson was the son of Jack Robinson and Lurline Robinson (née Cross). He was educated at Christchurch Boys High School, and then studied at the University of Canterbury, graduating Master of Science with second-class honours in chemistry in 1962. He completed a PhD at the same institution in 1964. His thesis, titled Studies in the coordination chemistry of certain transition metals', elucidated the first structure of a cluster compound and its unusual delocalised bonding.
On 12 May 1962, Robinson married Judith Rae, and they went on to have four children.