Grant was born in Mbabane, Swaziland, and educated in Waterford Kamhlaba School. At the age of nine, Grant witnessed an adulterous relationship between his mother and another man which subsequently led to the break-up of his parents' marriage. At this moment, he started keeping a diary and has done so ever since. He wears a watch on each wrist, one given to him by his dying father, permanently set on Swaziland time. .He studied English and Drama at the University of Cape Town, South Africa, and moved to London in 1982. He married Joan Washington in 1986 and has one daughter with her, Olivia, and a step-son, Tom.

Grant is a successful author, with works such as By Design calling on his Hollywood experience. He was also for a time the face of the Argos TV commercials. He has played The Doctor from Doctor Who twice, albeit unofficially on both occasions. In the comedy sketch Doctor Who and the Curse of Fatal Death, he portrayed a version of the Tenth Doctor, referred to as the Quite Handsome Doctor. He also voiced a version of the Ninth Doctor for the BBC original animated webcast Scream of the Shalka. Grant was also rumoured to be a possible choice for the Doctor as part of the series' resurrection in 2005, yet both his Doctor Who appearances are deemed to be non-canon.

He wrote and directed the 2005 film, Wah-Wah, loosely based on his own childhood experiences. In 2007, Grant will star in the movie adaptation of Irvine Welsh's best-selling novel Ecstasy: Three Tales of Chemical Romance.

Grant will appear as "The Voice" in 2+2+2 at American Nights at The King's Head Theatre, from July 3 to July 29, 2007.

On December 1st 2006 Richard E Grant turned real life investigator when with the help of the BBC Newsnight programme he exposed a $98 million scam to sell a bogus AIDS cure.

Grant is a teetotaler. After casting him as the alcoholic Withnail, director Bruce Robinson made Grant drink a bottle of vodka in one sitting so that he had experience of the sensation.