Directed by Italian filmmaker Paolo Sorrentino, the show is a co-production by Sky, HBO and Canal+.
In 2014, his film The Great Beauty took home the Oscar for Best Foreign Language Film.
Sorrentino has described The Young Pope as a story of "faith" and how people "handle and manipulate power".
He went on to say it is also about: "The clear signs of God's existence.
The clear signs of God's absence. How faith can be searched for and lost."
Oscar-winner Diane Keaton has also signed up to star alongside Law, as a nun called Sister Mary.
Keaton won the best actress Oscar in 1977 for Annie Hall, but shot to fame in The Godfather in 1972, playing the wife of Al Pacino's mafia boss.
Her career includes other successful roles in The First Wives Club and Marvin's Room.
- PAA