Yes. The Prophet Muhammad (SAWA) used to fast the day of his birth which teaches us to celebrate his birthday. The Hadeeths that he used to fast his day of birth are mentioned in many Sunni books like ( Saheeh Muslim, al-Bayhaqi, al-Tirmithi, Ibn Maajah, Al- Nasaa'ee, Ahmad ibn Hanbal and many others.).
'Sunni books narrated also that the Prophet (SAWA) used to celebrate the birthdays of pervious prophets like Moosa. This is another evidence that celebrating his birth anniversary is very good and a prophetic Practice ((Sunna).