Walsh, who will direct a script written by Richard Curtis, has worked on children's programming and soap opera Eastenders for 21 years. Her other credits include Funland, The Tudors, and Talk To Me.
The announcement was made by BBC One controller Charlotte Moore at the Edinburgh TV Festival on Thursday (August 22, 2013).
She said: "It's an honour to have Dame Judi Dench and Dustin Hoffman starring in this wonderful new adaptation.
"It's absolutely stellar casting for one of the nation's favourite children's classics."
Dahl's classic novel, published in 1990, tells the story of the shy old Mr Hoppy (Hoffman) who lives alone in an apartment building. For many years, he has been secretly in love with Ms Silver (Dench), a woman who lives below him.
Unfortunately for retired bachelor Mr Hoppy, the target of his affections lavishes her love on someone else: her pet tortoise.
Filming of the movie will begin next Spring.
It's been a rollercoaster couple of years for Hoffman, who received critical acclaim for his directorial debut Quartet, though was diagnosed with cancer. He was successfully treated for the disease in 2013.
Judi Dench's character M was killed off in the latest James Bond movie Skyfall, the most successful British film of all time.
Dustin Hoffman Will Star In Esio Trot
Judi Dench Will Play Ms Silver in Esio Trot