The ex-Leeds Rhino and Great Britain scrum-half, 40, will read Tom Percival's Tilda Tries Again - about a girl who suddenly finds her world changed and things that were once easy more challenging - on International Day of Persons with Disabilities.
The news comes just days after the death of Scotland and Melrose rugby legend Doddie Weir, who passed away at the age of 52 after battling MND for five years. A service was recently announced for Melrose Parish Church on Monday, December 19.
Burrow will read an inspirational tale about how Tilda finds a new way to approach her problems - and believe in herself.
It will be the first time on the BBC children's show a story is read using the special eye-controlled gear, which is able to recreate a version of Burrow's Yorkshire accent.
The sports star, diagnosed in 2019, said: "I used to love reading to my own children as part of their bedtime routine. I was so excited and honoured to be given the opportunity to read a CBeebies Bedtime Story.
"Reading and literacy are so important. It doesn't matter what your disability is, reading is accessible to everyone.
"Anyone can enjoy reading and develop a love of books and bedtime stories, just like me and my family."
Burrow was accompanied into the CBeebies studio by his wife Lindsey and two of the pair's children, Maya, seven, and Jackson, three.
The youngsters directed their father from the TV gallery, helped count down and shouted "action" when the cameras started rolling.
Burrow will follow in the footsteps of England and Tottenham striker Harry Kane, who appeared on the popular show in October to read a story about overcoming fear and finding one's inner lion through self-belief.
Singer Harry Styles, Captain America star Chris Evans, Foo Fighters frontman Dave Grohl and British actor Tom Hiddleston have also appeared on CBeebies Bedtime Stories.
Tilda Tries Again will be read by Burrow on CBeebies Bedtime Story at 6.50pm on Saturday December 3.