Preparing for the eventual extinction of its DVD-by-mail rental service, Netflix Inc. on Tuesday is introducing its first solution for subscribers who want entertainment delivered directly to their television sets with just a few clicks on a remote control.

The breakthrough comes in the form of 5-inch-by-5-inch device tailored for a year-old service that uses high-speed Internet connections to stream more than 10,000 movies and TV shows from Netflix’s library.

Although it’s provided at no additional cost to most of Netflix’s 8.2 million subscribers, the streaming service has had limited appeal so far because it doesn’t include the latest movies and couldn’t easily be watched on anything but a personal computer.

At $99.99, the Netflix set-top box is priced like a DVD player and is just as simple to hook up to a television. A high-speed Internet connection can either be plugged into the box or the device can pick up a wireless signal.