Murphy publicly apologised to the 'Sex On Fire' band last week, following an outburst earlier in the year when he branded the group "self-centred assholes" for their refusal to let him use their songs in an episode of Glee.
Speaking to Rolling Stone at California's Coachella music festival last weekend, Kings of Leon frontman Caleb Followill admitted: "I'm glad he said something. We don't hold grudges."
Drummer Nathan Followill added: "I'll just be glad when I can check my Google alerts and don't have to read anything about us and Glee. That'll be a wonderful feeling."
It was recently revealed that Glee will include more original material following the US chart success of 'Loser Like Me'.
Glee returns in the US on April 19 at 8/7c on Fox. The show continues in the UK on Mondays at 9pm on E4.
Listen to 'Loser Like Me' below: