The 90-minute BBC One show, which starts filming in London next spring, is based on Dahl's book Esio Trot.
Hoffman plays the retired bachelor Mr Hoppy, who is secretly in love with his neighbour Mrs Silver, played by Dame Judi, who lavishes all her affection on her pet tortoise Alfie.
BBC One controller Charlotte Moore 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."
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