The streaming service made the announcement Thursday alongside a video featuring Douglas and Arkin talking about the series over dinner.
"The thing I like most about the show is how you go from a funny moment, the way life is, you have a funny moment to tragedy," Douglas says in the clip.
The Kominsky Method, which debuted in November, follows Douglas as aging actor Sandy Kominsky with Arkin as his longtime agent Norman Newlander. The pair navigate Los Angeles together as they deal with aging and hardships.
The series hails from sitcom veteran Chuck Lorre (The Big Bang Theory, Two and a Half Men) who wrote the eight-episode first season alongside Al Higgins and David Javerbaum. Lorre and Higgins also serve as executive producers alongside Douglas.
Douglas won a Golden Globe for Best Actor in a TV Comedy for his role on the show which won Best TV Comedy.