The accident, involving a Route N98 bus, happened at about 02:00 BST at the street's junction with Harewood Place.
Emergency crews tried to help the injured man, aged in his 30s, but he was pronounced dead at the scene at 02:04. His next of kin have yet to be informed.
The bus driver stopped at the scene and is assisting with police inquiries. The driver has not been arrested.
Formal identification and a post-mortem examination is expected to be carried out in due course.
Officers from the Serious Collision Investigation Unit are investigating and anyone with any information about what may have happened leading up to the crash is asked to contact them.
A man has died after being hit by a bus on Oxford Street in central London.