He was born Eric Alexander Rennie in Bradford, Yorkshire, England. He had several other jobs before gaining employment as a stand-in in an Hitchcock film of 1936. Acting then became his profession but it was some years before he found success as a leading man in the cinema, his exceptional height and chiselled features standing him in good stead. In 1945 he played a major role in the original version of The Wicked Lady, starring Margaret Lockwood and James Mason. From that point on he was a star and shortly afterwards he moved to the USA where, in the early 1950s, he had significant roles in several major productions of the 20th Century Fox studio.

In 1959 Rennie became a familiar face on television taking the role of Harry Lime in The Third Man, a spin-off TV series from the film starring Orson Welles. During the 1960s he continued his TV career with guest appearances on such series as Route 66, Alfred Hitchcock Presents, Perry Mason, Wagon Train, Lost in Space, The Time Tunnel, Batman, The Invaders, and The F.B.I.

Both his marriages ended in divorce. His second marriage was to actress Maggie McGrath. Their son David Rennie was rumoured to be the result of her illicit affair with another Hollywood actor. He also had a son, John Marshall, to his long time friend and mistress Renée Gilbert.

He moved to Switzerland in the latter part of his life. However, it was during a 1971 visit to his mother at Harrogate Yorkshire, following the death of his brother, that he died from emphysema.

John Rennie, the designer and builder of the original Waterloo Bridge, was his great great grandfather.