Tony King, 29, pleaded guilty to second degree murder in the strangulation death of Michael Bozarth in June of 2013 inside their Buchanan County jail cell.
Workers at the jail found Bozarth in the cell after hearing commotion from other inmates.
In July, King was sentenced to life in prison for killing his 7-year-old son in 2012, then setting their Harrison County home on fire.
Bozarth, a registered sex offender, was serving time for statutory sodomy.
King's sentencing is set for October 31. He could face up to 20 years for Bozarth's death.