The eight-part drama is to premiere later this year.
It follows the royal from her accession to the throne at the age of 18 through her courtship and marriage to Prince Albert, played here by Tom Hughes.
"The series chronicles the public and private life of one of history's most interesting and influential monarchs," the British broadcaster promised in a press release.
Coleman is best known for her roles on TV's Doctor Who and in the current big-screen romance Me Before You.
Sewell's credits include the films Gods of Egypt, Hercules and Abraham Lincoln: Vampire Hunter, and the Amazon series Man in the High Castle.