The actor will read Fleabag by Helen Stephens, which is about the friendship between a young boy and his scruffy pet.
He recorded the story last year with Woody next to him and says the broadcast will be a fitting mark of respect to the memory of his dog.
Tom Hardy spoke about his loss in an emotional blog at the time.
He revealed he first bonded with Woody when he found him as a stray running towards a motorway while he was filming Lawless in Atlanta in the US.
After rescuing him, Tom regularly took him to film sets and red carpet premieres and Woody even appeared in Peaky Blinders.
Fleabag tells the story of a dog who needs a home and a boy who wants a dog.
One day they find each other and Fleabag finally gets the loving home he's been looking for.
The story will air on National Dog Day on 26 August.
Tom Hardy, 39, read Odd Dog Out, There's a Bear On My Chair, the Cloudspotter and You Must Bring a Hat on his other Bedtime Story appearances.
A range of celebrities have been involved with CBeebies' Bedtime Story strand including actor Damian Lewis, astronaut Tim Peake and Great British Bake Off winner Nadiya Hussain.
CBeebies Bedtime Stories is on CBeebies every day at 6.50pm.