Hopkins, 82, asked viewers to look forward to 2021 after "a tough year, full of grief and sadness for many, many, many people," in the video posted Tuesday.
"Forty-five years ago today, I had a wake-up call. I was headed for disaster, I was drinking myself to death. I'm not preachy, but I got a message," said the actor, best known for playing serial killer Hannibal Lecter.
"A little thought that said, 'Do you want to live or die?' And I said, 'I want to live.' And suddenly the relief came and my life has been amazing."
Hopkins acknowledged that he also has difficult moments: "I have my off days and sometimes little bits of doubt and all that."
And he called on people to stay positive: "All in all, I say hang in there. Today is the tomorrow you were so worried about yesterday. Young people, don't give up. Just keep in there. Keep fighting. Be bold. Mighty forces will come to your aid. That's sustained me through my life."
In March, Hopkins posted a video of himself playing the piano to his cat, Niblo, on Twitter.
Hopkins is a keen composer of classical music and released an album of his musical works in 2012.
He was nominated for a Best Supporting Actor Oscar in 2020, for his role as Pope Benedict XVI in the Netflix film "The Two Popes."