Riot has indicated that they will not "eavesdrop" and will only review the recordings if a special request is sent. The rest of the files are to be stored temporarily and will be deleted later, just like text chat logs.
"We want all of our games to be safe and inclusive for everyone who chooses to play themWe know disruptive behavior using our voice chat is a concern for a lot of players, and we’re committed to addressing it more effectively."
Testing of the solution will begin on servers in North America. It is not known when voice chat recording will be introduced in other regions. The company does not exclude the possibility that this solution will also appear in their other games.