Harry Andrews was born on 10 November 1911, in Tonbridge, Kent. He was the son of Henry Arthur Andrews, a General Practitioner, and Amy Diana Frances (née Horner). Andrews attended Yardley Court school in Tonbridge, and Wrekin College in Wellington, Shropshire. From October 1939 to October 1945, Andrews served with the Royal Artillery during the Second World War. From 1956 to 1961 he lived in the family home, Little Thatch, Belgrave Road, Seaford. Andrews died at the age of 77 on 6 March 1989, at his home in Salehurst, leaving behind his long-term friend and partner Basil Hoskins. They are now buried alongside each other at St Mary the Virgin's Church, Salehurst.

Andrews made his first stage appearance in September 1933 at the Liverpool Playhouse playing John in The Long Christmas Dinner. He made his London debut in March 1935 at the St James's Theatre playing the role of John in Worse Things Happen at Sea. In March 1936 he starred alongside Paul Robeson, Orlando Martins and Robert Adams in the production of the play Toussaint Louverture by C.L.R. James at the Westminster Theatre in London. In October 1936, Andrews made his first appearance in New York playing the role of Horatio in Hamlet at the Empire Theatre. From September 1937 to April 1938, Andrews worked with John Gielgud's company at the Queen's Theatre, appearing in such shows as Richard II, The School for Scandal and The Merchant of Venice. In 1939, Andrews assumed the role of Laertes in a production of Hamlet at the Lyceum Theatre. This was the final production at the Lyceum before it closed, though it was restored in 1996.

Prior to his film career, Andrews was an accomplished Shakespearean actor, appearing at such venues as the Queen's Theatre, the Lyceum Theatre, and the Shakespeare Memorial Theatre in the UK as well as theatres in New York City, Paris, Antwerp and Brussels. Andrews made his London theatre debut in 1935 at the St James's Theatre and his New York debut in 1936 at the since-demolished Empire Theatre.

In December 1945, one month after returning from Service in the Second World War, Andrews appeared with the Old Vic company at what was then referred to as the New Theatre, succeeding George Curzon in the parts of Sir Walter Blunt in Henry IV, Part 1, Scroop in Henry IV, Part 2, Creon in Oedipus and Sneer in The Critic. The company toured to New York City in the summer of 1946, appearing at such venues as the Century Theatre. Upon returning to Britain in September 1946, Andrews continued performing with the Old Vic company through the end of the 1948–1949 season.

In 1949, Andrews joined the company at the Shakespeare Memorial Theatre in Stratford-upon-Avon, in which he performed in such Shakespearean roles as Macduff, Don Pedro and Cardinal Wolsey. Andrews toured with the company through Australia in 1949. He continued to perform with the company in Stratford-upon-Avon through the 1951 season, playing Henry IV through three consecutive Shakespeare plays. He then travelled to New York with the company of Laurence Olivier, performing in such plays as Caesar and Cleopatra and Antony and Cleopatra at the Ziegfeld Theatre. Andrews went on tour with the Old Vic company performing Henry VIII in Paris, Antwerp and Brussels.

Andrews was known for his portrayal of tough military officers. These performances included Sergeant Payne in A Hill in Korea in 1956, Major Henry in I Accuse! in 1958, Major Swindon in the 1959 film adaptation of George Bernard Shaw's play The Devil's Disciple, Captain Graham in A Touch of Larceny in 1959, Lord Lucan in The Charge of the Light Brigade (1968) and Colonel Thompson in Too Late the Hero in 1970, and Grand Duke Nicholas, commander of the Russian army, in Nicholas and Alexandra in 1971.

In addition to film work, Harry Andrews also appeared in several television series. In the early 1960s, Andrews appeared in two episodes of Armchair Theatre. In 1975, he played Colonel Bruce in Edward the Seventh. The following year, Andrews portrayed Darius Clayhanger in a television series based on The Clayhanger Family novels. In 1985, Andrews was interviewed on an episode of the documentary series This Is Your Life. In 1978, he played one of the Kryptonian elders during the sentencing of the three villains in the film Superman.