Born in London, he was the grandson of the first Baron of Chelmsford. Educated at Marlbrough College and the Slade, with aspirations of becoming a painter. However (though he remained an accomlished watercolor artist) he quickly turned to the theatre, making his first appearance on stage in a production of Colonel Smith in 1909 at St James's Theatre.
He put his career on hold when, in 1914, he enlisted as a private in the first World War (originally hoping to join a Scottish regiment because he wanted to wear a kilt). He did see some action in the trenches but had to be sent home after being wounded.
He made his first film appearance in 1916 with The Real Thing at Last (1916) and afterwards returned to the theatre with A Little Bit of Fluff which ran for over 1200 performances and led to him appearing in a film adaption. In 1925 he appeared in Noel Coward's production of On With the Dance where he got to show off his knack for camp performances by playing one of two elderly women sharing a boarding house.
In the early 30s his old friend, actor turned director, James Whale requested his friend to join him there to play the role of Horace Femm in his upcoming production of The Old Dark House (1932). Thesiger agreed and the film became a huge success. He returned to Britain to make The Ghoul (1933) with Boris Karloff. Whale requested Thesiger's services in Hollywood again, this time to appear in his sequal to Frankenstein (1931), and Bride of Frankenstein (1935).
He returned to Britain and, unfortunately, never worked with Whale again. He appeared in the Alexander Korda produced The Man Who Could Work Miracles (1936) and had a memorable role in the tongue-in-cheek horror They Drive by Night (1938). In the 40s he appeared with Will Hay in My Learned Friend (1943) and Don't Take It to Heart (1944).
His other notable films of the 40s include The Chronicle History Or King Henry the Fift with His Battell Fought at Agincourt in France (1944) and The Winslow Boy (1948). He returned briefly to America to appear in As You Like It on Broadway and afterward divided his time between theatre and film. Notable later films include Last Holiday (1950), Laughter in Paradise (1951), Scrooge (1951) and The Man in the White Suit (1951).
He made his last film appearance in The Roman Spring of Mrs. Stone (1961) and his last stage performance, opposite Sirs Ralph Richardson and John Gielgud, in a production of The Last Joke. He died in London, of natural causes, shortly afterwards on the eve of his 82nd birthday.