Congratulations on your new baby in spanish

¡Felicitaciones por el nacimiento de su bebé! (Congratulations on the birth of your baby!)

Other ways to express congratulations on a new baby in Spanish:

Note: In Spanish-speaking countries, it's common to use the formal "you" (usted) when addressing someone, especially if you don't know them well. So, if you're speaking to someone you don't know well, you might say "Felicitaciones por el nacimiento de su bebé" instead of "¡Felicitaciones, bebé!"