The "Slumdog Millionaire" filmmaker will executive produce and direct the 10-episode series, titled "Trust", alongside writer Simon Beaufoy and Christian Colson.
The series was picked up by bosses at American network FX last year, but casting is only now underway.
Production is slated to begin in London in June and the show will premiere in January next year.
The series will start off in 1973 and will centre on Getty III's kidnapping.
During the ordeal, Getty III's mother Abigail Harris begged oilman John Paul Getty, Sr. To pay the ransom, which he initially refused. He eventually agreed to pay up and his teenage grandson was subsequently freed.
This is the second project in development about Getty III's kidnapping - Ridley Scott has reportedly signed on to direct a movie version, titled "All the Money In the World."
Casting details have yet to be revealed, but he is said to be keen to land Natalie Portman to portray Harris, and Jack Nicholson to play Getty Sr.
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