Reported yesterday, changes undergone by the iTunes Store terms and conditions referenced an “Apple TV 3.0 Software Update,” with Softpedia noting that Apple was likely to issue the new software as early as this week. As expected, Apple has indeed launched the new software, introducing a redesigned main menu that makes navigating content simpler and faster, iTunes Extras and iTunes LP, Genius Mixes and Internet radio, and more.

“The new software for Apple TV features a simpler and faster interface that gives you instant access to your favorite content,” Eddy Cue, Apple’s vice president of Internet Services, said. “HD movies and HD TV shows from iTunes have been a huge hit with Apple TV customers, and with Apple TV 3.0 they get great new features including iTunes Extras, Genius Mixes and Internet radio.”

According to Apple, recently rented or purchased movies, as well as other content including TV shows, music, podcasts, photos and YouTube, are now accessible directly from the new main menu. The redesigned user interface makes navigating your favorite content even simpler and faster, according to the release notes posted on Apple’s Support section.

iTunes Extras enables the viewing of stunning, full-screen, additional content for select movies, including deleted scenes, interviews, and interactive galleries, while iTunes LP provides full-screen additional content for select music albums, including live performance videos, lyrics, artwork, liner notes, interviews, photos, and more.

Genius Mixes, a feature recently introduced by Apple with the latest iTunes version, allows users to enjoy endless mixes of songs from their iTunes library that go great together, the company explains. This feature also made it into the Apple TV 3.0 Software Update. The aforementioned Internet Radio feature is also noted by Apple as a key plus, as it lets set-top-box owners browse thousands of stations and enjoy them directly on their TV. Users can also tag favorite stations for later listening, the changelog reveals.

Other new additions include Local Music Search (search your local music library with a few clicks of the remote); iPhoto Events and Faces (simplify finding your favorite photos from iPhoto); and YouTube in HD (enjoy hundreds of thousands of YouTube videos in stunning HD).