However, Riot have taken their sweet time: since the original announcement, Wild Rift has come out in Europe, the Middle East & North Africa, Russia, Turkey—essentially everywhere that's not North America. If you go into the Google Play Store now, you will see that it is up there, but only allowing you to "pre-register for a chance to get early access to the game."
It seems we've got an update from Riot at last, as well as a solid (beta) release date: on March 29th, you will be able to sign up for an open beta version on both iOS and Android in the Americas. There is no confirmed date for the official release of the alpha version of the game, but it's sure to come soon. The game will be free to play (as is the limited beta version), and Riot promises to compensate for the long waiting time with a special event (details unspecified) as well as "tons of Blue Motes, XP, champions, and even exclusive content from long expired events."
Named after the Summoner's Rift map in the PC version, Wild Rift will be set up for shorter and faster gameplay on the go—that is, optimizing the layout and style while staying true to its signature MOBA format. Riot's announcement warns, however, that because the Americas servers use a completely different infrastructure from the rest of the world, players will be unable to match with players outside of North and South America if that is where their account is situated, even if they are abroad.