From Sahih Bukhari (Hadith 4807):
Narrated Al-Awwam:I asked Mujahid regarding the prostration in Surat Sa`d. He said, "I asked Ibn `Abbas, 'What evidence makes you prostrate?' He said, "Don't you recite:--'And among his progeny, David and Solomon..(6.84). Those are they whom Allah had guided. So follow their guidance.' (6.90) So David was the one of those prophets whom Prophet (Muhammad) was ordered to follow. David prostrated, so Allah's Messenger (ﷺ) (Muhammad) performed this prostration too
Reference: Bukhari 4807