SAN FRANCISCO  Owners of the Nintendo Wii can finally stop waving their video game controllers in the air and sink back onto the couch.

Nintendo is bringing Netflix’s online streaming video service to its Wii gaming console, the most popular in the industry, the companies plan to announce Wednesday. The service lets subscribers choose from a catalog of generally older movies and television shows and watch them instantly.

The deal is further evidence of a movement by makers of game consoles to broaden their appeal by positioning them as a bridge between the living room television and a wider world of online multimedia.

So far those efforts have not been enough to calm anxieties about the overall direction of the $16.8 billion video game business. The industry is threatened by a dearth of popular new franchises, which tend to attract gamers to an endless number of sequels, as well as the sudden rise of cheap games for smartphones and free casual games on social networks.