"To all of those who have asked, I will not be going to the Inauguration on January 20th," the president tweeted.
Mr Trump is facing calls for his removal from office after five people died when a mob of his supporters invaded Congress.
The latest death is that of US Capitol Police officer Brian Sicknick, who succumbed to his injuries in hospital.
Wednesday's violence came hours after Mr Trump encouraged his supporters to fight against the election results as Congress was certifying Mr Biden's victory in the November vote.
Under pressure, Mr Trump finally released a recorded statement late on Thursday condemning the storming of the US Capitol as a "heinous attack".
It is highly unusual but not unprecedented: the last president to skip the inauguration of his successor was Andrew Johnson, in 1869.
Mr Trump has now admitted defeat in the 3 November election and has promised a peaceful transfer of power. However, he has repeated baseless claims of widespread voter fraud.