Rotheram was born in Hexham, the son of John Rotheram M.D. Shortly afterwards his father moved to Newcastle where he was physician at the infirmary for many years. Edward was the brother of John Rotheram (q.v.).,
He joined the navy in 1777, served in the West Indies and was present aboard Culloden on the 'Glorious First of June' in 1794. He rose to be captain and commanded Royal Sovereign, Admiral Collingwood's flagship at Trafalgar in 1805. It was said that there was some friction between him and Collingwood which Nelson removed, saying that in the presence of the enemy, all men should be brothers. Rotheram later commanded Bellerophon in the Channel until 1808, but received no further command.
Although Collingwood had a poor opinion of his abilities, Rotheram's detailed account of the personnel of Bellerophon ('Billy Ruffian') has, ironically, proved an invaluable document for researchers of Nelson's navy.