Amazon announced a new slate for its streaming service which will include the two unmissable shows, each with a big-name cast.
Corden is set to star in Mammals, a six-part comedy drama from Olivier and Tony-award winning Jez Butterworth, who worked on Spectre.
Few details have been released on the plot of the series, but first-look pictures showed Corden in character as Jamie, alongside his castmates Sally Hawkins, Colin Morgan, Melia Kreiling, Henry Lloyd-Hughes and Samuel Anderson.
Butterworth said: "You’ll enjoy this if you enjoy James, Sally and my work. It’s a relationship drama but also a whodunit."
Meanwhile, a creepy trailer gave a flavour of new Capaldi thriller The Devil's Hour, where the former Doctor Who star appears alongside Jessica Raine.
The series features strange goings-on in the so-called "devil's hour", between 3am and 4am, which sees Raine's character Lucy wake up at 3.33am on the dot every night of her life to terrifying visions.
With her eight-year-old son listless and emotionless, her mother talking to empty chairs and her house haunted by the echoes of someone else's life, Lucy starts to find answers after her name is inexplicably connected to a string of brutal murders in the area.
Meanwhile, Capaldi's character is a reclusive nomad driven by a murderous obsession who becomes the prime target of a police manhunt led by detective Ravi Dhillon, played by Nikesh Patel.
Capaldi said of his character Gideon: "The nature of the piece is spectacularly dark and has been enjoyable to play. He is a character that has fallen through the cracks and is responsible for some serious crimes. But he is not what he appears. He belongs to the night."
Both series are due to air on Prime Video later this year.
Watch: James Corden pays tribute to Kay Mellor