Rennie was born in Bradford, Yorkshire, England, and had several other jobs before gaining employment as a stand-in in a 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 he appeared in such classics as
1959, Rennie became a familiar face on television, taking the role of Harry Lime in The Third Man, a spin-off series from the film starring Orson Welles. In the same year, he returned to the UK permanently, and eventually died at Harrogate in his home county of Yorkshire.