A Young Doctor's Notebook is based on a collection of short stories by Russian writer and playwright Mikhail Bulgakov.
Hamm will play the older doctor, who will be seen conversing with his younger self, played by Radcliffe.
22-year-old Radcliffe said: "I have been an obsessive Bulgakov reader for a couple of years now so when the opportunity to become involved in this project came up, I could barely contain my excitement.
"The book is funny, grotesque and heartfelt in equal measure and I look forward to working with a great group of people to help bring it to life."
Hamm added: "I am thrilled to get the opportunity to work on such rich source material with such fantastically talented people whose work I greatly respect, and to continue the relationship with Sky who have taken such good care of Mad Men since acquiring it."
Produced by Big Talk Productions in association with Jon Hamm and Jennifer Westfeldt's Point West Pictures, the four-part series will recount Bulgakov's semi-autobiographical experiences as a young doctor working in the small village of Muryovo at the dawn of the Russian Revolution in 1917.
"Clelia Mountford and Big Talk have been championing this project unabashedly and I share their great enthusiasm for bringing something original, dark, funny and moving to light," said Hamm.
"Also, I have been watching Bridget Jones's Diary on infinite loop, and I think I've finally got this accent thing sorted..."
A Young Doctor's Notebook will broadcast on Sky Arts in 2013 and will be distributed internationally by BBC Worldwide.