Born in Scone in Perthshire in 1955, Robertson was brought up on the north-east coast of Scotland, but has spent most of his professional life in London. After working as an editor at Penguin Books and Secker and Warburg, he became poetry and fiction editor at Jonathan Cape.
Robertson's poetry appears regularly in the London Review of Books and The New York Review of Books, and is represented in many anthologies. In 2004, he edited Mortification: Writers' Stories of Their Public Shame, which collects seventy commissioned pieces by international authors. He published The Deleted World in 2006, "versions" of the Swedish poet Tomas Tranströmer (drawing on translations by Robin Fulton and others), and a new translation of Medea. He has two daughters, Ellie, 19, and Cait, 17.
Robertson is a trustee of the Griffin Trust for Excellence in Poetry.
Robertson's first volume of poetry, A Painted Field, won the 1997 Forward Prize for Best First Collection and the Scottish First Book of the Year Award. Slow Air followed in 2002, and his third book, Swithering, was published in 2006, winning the Forward Prize for Best Collection. He completed the set of Forward Prizes in 2009 when 'At Roane Head' won the award for Best Single Poem. This poem is included in his fourth collection, The Wrecking Light (2010).
In 2004, Robertson received the E. M. Forster Award from The American Academy of Arts and Letters. In 2009 he was elected a Fellow of the Royal Society of Literature