Inmates in Oklahoma state prisons will soon connect to the outside world through Securus Technologies, a Texas-based prison communications company that has paid out millions over the past four years to settle claims that it illegally recorded phone conversations between inmates and attorneys.

Securus has also faced multiple class-action lawsuits from family and friends of inmates who say the company excessively charged them between $9.99 and $14.99 for a 15-minute call.

In a July 29 Facebook post, the state Department of Corrections announced Securus won a contract bid and would replace Global...