The 76-second clip -- which has gotten nearly 3 million "likes" since it was posted on Tuesday -- features a new outdoor photo of Harry smiling with his infant son Archie, who is wearing a knit hat with pom poms.
Set to Coldplay's "Viva La Vida," the montage also shows dozens of snap shots from the royal couple's work and travels, as well as images of baby Archie.
"Wishing you all a very Happy New Year and thanking you for your continued support! We've loved meeting so many of you from around the world and can't wait to meet many more of you next year. We hope 2020 brings each of you health and continued happiness," the couple wrote in their post.
The duke and duchess of Sussex spent their first Christmas with their 7-month-old son in Canada.