The show, starring Halle Berry, is about an astronaut, who comes home after spending a year alone in space, and tries to reconnect with her husband and son.
CBS will start screening the show in June and Amazon will be allowed to stream episodes four days later.
The exclusive service is free for subscribers to Amazon’s Prime Instant Video program on Kindle and gaming platforms.
Amazon has similar deals with PBS for the British drama series “Downton Abbey”.
The stock of both companies were flat in morning trade on Wednesday.
Reporting by Chandni Doulatramani in Bangalore; Editing by Savio D'Souza