John Edelsten was born on 12 May 1891, the third son of John Jackson Edelsten, a tea broker, and his wife, Jessica. In 1904 he entered the Royal Naval College, Osborne [Isle of Wight] and after passing on to Dartmouth [Devon] two years later, then joined HMS Hibernia, as a midshipman in 1908, later serving with the cruiser HMS Natal and the battleship HMS London.

Edelsten became a sub-lieutenant in 1911 and was promoted lieutenant at the end of 1913 while serving with the destroyer HMS Swift. He joined the light cruiser HMS Yarmouth in March 1914 and served in her with the Grand Fleet until the end of 1917. Showing particular talent at signals, Edelsten became flag lieutenant to Admiral Sir Thomas Hurt, Commander-in-Chief, South America station, (1919-1921), and at the end of 1921 was promoted to lieutenant-commander. He then joined HMS Delhi as a staff officer to Rear-Admiral Sir Hubert Brand, commanding the 1st Light Cruiser Squadron. Edelsten served in the cruisers HMS Carysfort and HMS Comus before becoming commander at the end of 1926. Briefly leaving the sea, Edelsten next taught on the staff course at Greenwich (1928-1930), before joining the cruiser HMS London to serve in her for two years. On 14 December 1926 he married Frances Masefield. They had no children.

On 30 June 1933, Edelsten was promoted again, to captain, and in 1935 commissioned the new light cruiser HMS Galatea before becoming the Admiralty's deputy director of plans at the beginning of 1938. He returned to active service in the cruiser HMS Shropshire in March 1940, serving on trade protection duties in the south Atlantic and Indian oceans. In 1940–41 he was senior naval officer in the operations against Italian Somaliland [later Somalia]. Edelsten then became Chief of Staff to Admiral Sir Andrew Cunningham, Commander-in-Chief, Mediterranean Station, a position which he held until the end of 1942, after being promoted Rear-Admiral.

Edelsten then returned home as assistant Chief of Naval Staff, with special responsibility for anti-U-boat warfare and trade defence, at the height of the battle of the Atlantic. In 1945 he became Rear-Admiral, Destroyers, in the new British Pacific Fleet (BPF). Edelsten was promoted to Vice-Admiral later in the year and in October 1945 was appointed to command the 1st Battle Squadron. At the end of the year he moved to command the 4th Cruiser Squadron but was soon recalled to the Admiralty, serving from late 1946 as an adviser to the Deputy Chief of Naval Staff and then becoming Vice-Chief of Naval Staff in 1947. He became a full admiral in February 1949 and was appointed as Commander-in-Chief, Mediterranean in 1950. His final position was as Commander-in-Chief, Portsmouth, (1952-1954), when he was also the first NATO Commander-in-Chief of the Channel Command. He was to be the next Commander-in-Chief, Home Fleet, but retired on 24 November 1954.

Edelsten was made CBE in September 1941 for his services off Somaliland. He was appointed CB in June 1944 and was knighted in June 1946. He was promoted GCB in January 1953. He died on 10 February 1966.