Hozier wrote a statement on his Facebook page saying there were no hard feelings.
"What was sought from my end was an apology and redaction of an unfair inferral," he said.
"I will continue to follow and respect his work and look forward to moving on from this issue."
It was initially reported that Hozier had filed a defamation lawsuit against Chilly Gonzales.
The rocker scored a huge breakout hit with the Grammy Award-nominated Take Me to Church, which he originally released in 2013, but Gonzales recently stirred controversy by claiming Hozier's tune was identical to the track he produced for fellow Canadian, Feist, in 2011.
- WENN