In the video obtained by the Sun and TMZ, the singer can be seen telling an offensive joke while sat backstage at a promotional event when he was 15.
"As a young man, I didn't understand the power of certain words and how they can hurt," Justin, 20, has said in a statement.
"I thought it was ok to repeat hurtful words and jokes, but didn't realise at the time that it wasn't funny and that my actions were continuing the ignorance.
"Thanks to family and friends I learned from my mistakes and grew up and apologised for those wrongs. Now that these mistakes from the past have become public I need to apologise again to all those I have offended. I'm very sorry."
The star continued, "I take my friendships with people of all cultures very seriously and I apologise for offending or hurting anyone with my childish and inexcusable mistake. I was a kid then and I am a man now who knows my responsibility to the world and to not make that mistake again.
"Ignorance has no place in our society and I hope the sharing of my own fault can prevent others from making the same mistake in the future.
"I thought long and hard about what I wanted to say, but telling the truth is always what's right. Five years ago I made a reckless and immature mistake and I'm grateful to those close to me who helped me learn those lessons as a young man. Once again, I'm sorry."