What’s “Happy new year” in Japanese?

In Western countries you say “Happy new year” or “Happy holidays” around this time of the year. In Japanese there are two expressions equivalent of “Happy new year”.

akemashite omedeto.

“Akemashite” means that a new year, day or season begins. Therefore, this is a greeting for celebrating a new year start. "Omedeto" is congratulations.

yoi otoshi o.

“Mukaete kudasai” should follow this, but it is omitted. The meaning of “mukaete”(mukaeru) is that the time is approaching. "Yoi" is good. "Toshi" is a year and it is preceded by honorific "o". The whole sentence conveys that you spend a good year end and greet the new year.

You should not say “akemashite omedeto” before the 1st of January. You say “yoi otoshi o” instead of good bye when you see off your friends or colleagues at the end of the year.