Stanley was born in Alderley, Cheshire, the son of Edward Stanley, rector of Alderley and later Bishop of Norwich. A brother was Arthur Penrhyn Stanley and his sister Mary Stanley.
He entered the Royal Naval College at the age of fifteen, and for nine years served under Phillip Parker King on HMS Adventure and John Franklin in the Mediterranean. In 1836 he sailed to the Arctic as scientific officer on HMS Terror under George Back. In 1838 he was given command of HMS Britomart and sailed to Australia and New Zealand, returning in 1843. In March 1842 he was elected a Fellow of the Royal Society

In December 1846 Stanley sailed from Portsmouth in charge of HMS Rattlesnake, with the purpose of surveying the seas around the Great Barrier Reef and Torres Strait. The ship called at Madeira, Rio de Janeiro, Simon's Town and Mauritius, arriving in Sydney in July 1847. Stanley died in Sydney on the return trip having accomplished the main objects of the voyage and was given a state funeral.

In memory of his brother, Dean Stanley of Westminster Abbey donated the font in ChristChurch Cathedral, Christchurch.