Here's the answer:
“おたんじょうびおめでとう”
(otanjōbi omedetō)
Watch a real native speaker say it:
Here's how it sounds in a textbook:
You could also say:
- お誕生日おめでとう
- 誕生日おめでとう
Fun fact: the hundreds of thousands of people learning Japanese with Memrise get this phrase correct 91.24% of the time!