The eight-part series will premiere in Britain before an American debut in 2013.
The drama focuses on the investigation of the murder of a young boy in a small coastal town. Tennant and Olivia Colman will play the lead detectives, while Darvill plays the town priest, the Reporter said.
Vicky McClure, Jodie Whittaker, Andrew Buchan and Will Mellor also star in the series.
"Broadchurch" is written and created by "Doctor Who" writer Chris Chibnall. Jane Featherstone is executive producer and Richard Stokes serves as producer.