The deal also includes popular BBC One dramas Last Tango in Halifax and Life on Mars and comedies The Office, Absolutely Fabulous, Outnumbered and Red Dwarf.
The retailer said the deal was part of its “continued investment in quality content for its members.”
Formerly Lovefilm, Amazon Prime Instant Video claims to offer “more than 15,000 films and TV shows” for unlimited streaming on a range of devices including tablets, smartphones and games consoles.