The actor is believed to have had terminal cancer, but his spokespeople have refused to confirm this.
A statement from his representative said: "We formally announce the loss of Leslie Grantham, who passed away at 10.20am on the morning of Friday 15th June 2018.
"His ex-wife and sons have asked for their privacy to be respected at this difficult time, and for there to be no approaches to them for information or comment.
"There will be a private funeral which will be attended by close family and friends only."