The actor, along with fellow stars Toby Jones and Patrick Stewart, will be heard on the station today reading selections for the original scripts of 70 years ago.
The reports began on the Today programme and will continue through the weekend, finishing on Sunday with Broadcasting House and The World This Weekend.
Two hundred pages of D-Day broadcasts, from what was then called the Home Service, have been published online, including reports by correspondents following the forces on land, air and sea.
Radio 4 controller Gwyneth Williams said: "A day of deep significance; a day that carries, in memory, unimaginable burdens for a nation. I am delighted to offer Radio 4 listeners this opportunity to understand D-Day anew.
"And not just through the broadcasts but now, Radio 4, in digital times, can open its treasure trove of a website and bring original radio scripts to life, recreating that day in greater intensity and immediacy for a new generation."