Educated at Eton College, Coote joined the Royal Navy in 1833 and served on the coast of Syria in 1840. He was made Commander of the HMS Volcano in 1851 while serving in the West Africa Squadron. Promoted to Captain in 1854, he commanded HMS Victory from 1860, HMS Gibraltar from 1864 and HMS Arethusa from 1867.
He became Commander-in-Chief, Queenstown in 1874 and Commander-in-Chief, China Station in 1878.
He retired in 1885. He is buried in Woking Cemetery. There is a memorial to him in Street Catherine"s Church in Tullamore in County Offaly.
Coote married Lucy Parry, daughter of the Arctic explorer Admiral Sir William Parry, in 1854. Coote died in March 1898, aged 77.